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Transcript of Polynomials
![Page 1: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/1.jpg)
POLYNOMIALSMs. Johnson 8th Grade Math
![Page 2: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/2.jpg)
KEY VOCABULARY Variable- A quantity that can change or vary,
taking on different values
![Page 3: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/3.jpg)
KEY VOCABULARY Variable- A quantity that can change or vary, taking on
different values
Constant- A quantity having a fixed value that does not change or vary, such as a number. A constant term does not contain a variable. [( y= 5 + x ) in this example, 5 is a constant
![Page 4: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/4.jpg)
KEY VOCABULARY Variable- A quantity that can change or vary, taking
on different values
Constant- A quantity having a fixed value that does not change or vary, such as a number. A constant term does not contain a variable. [( y= 5 + x ) in this example, 5 is a constant
Coefficient- A number that multiplies a variable [ (4b) in this example, 4 is a coefficient]
![Page 5: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/5.jpg)
KEY VOCABULARY Variable- A quantity that can change or vary, taking on
different values
Constant- A quantity having a fixed value that does not change or vary, such as a number. A constant term does not contain a variable. [( y= 5 + x ) in this example, 5 is a constant
Coefficient- A number that multiplies a variable [ (4b) in this example, 4 is a coefficient]
Like Terms- Terms whose variables and exponents are the same (the coefficients can be different) [5a + 8a ; or x2y + 3x2y]
![Page 6: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/6.jpg)
KEY VOCABULARY Monomial- a polynomial containing one term which
may be a number, a variable, or a product of numbers and variables, with no negative or fractional exponents
( -5, xy, 5x2, 5x2y3z )
![Page 7: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/7.jpg)
KEY VOCABULARY Monomial- a polynomial containing one term which
may be a number, a variable, or a product of numbers and variables, with no negative or fractional exponents
( -5, xy, 5x2, 5x2y3z )
Binomial- a polynomial containing two unlike terms ( x+ 5, xy + 5, 5x2 – x, 5x2 + y3)
![Page 8: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/8.jpg)
KEY VOCABULARY Monomial- a polynomial containing one term which
may be a number, a variable, or a product of numbers and variables, with no negative or fractional exponents
( -5, xy, 5x2, 5x2y3z )
Binomial- a polynomial containing two unlike terms ( x+ 5, xy +5, 5x2 – x, 5x2 + y3)
Trinomial- a polynomial containing three unlike terms
(x+5+y, 5x2 –x+y, 5x2 + y3 – z)
![Page 9: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/9.jpg)
KEY VOCABULARY Monomial- a polynomial containing one term which may
be a number, a variable, or a product of numbers and variables, with no negative or fractional exponents
( -5, xy, 5x2, 5x2y3z )
Binomial- a polynomial containing two unlike terms ( x+ 5, xy+5, 5x2 – x, 5x2 + y3)
Trinomial- a polynomial containing three unlike terms(x+5+y, 5x2 –x+y, 5x2 + y3 – z)
Polynomial- an expression that is a monomial or the sum of monomials (xy, xy- 5 , 5x2 – x + y, 5x2 + y3 – z +3)
![Page 10: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/10.jpg)
8.A.6 MULTIPLY MONOMIALS
Just remember the Product Law!
12a3b2 (3a4b6)
Product Law2 applies to the coefficients
Product Law1 applies to the variables
121a3b2 (31a4b6) =
![Page 11: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/11.jpg)
8.A.6 MULTIPLY MONOMIALS
Just remember the Product Law!
12a3b2 (3a4b6)
Product Law2 applies to the coefficients
Product Law1 applies to the variables
121a3b2 (31a4b6) = 361a7b8 = 36a7b8
![Page 12: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/12.jpg)
8.A.6 MULTIPLY MONOMIALS
Some examples:
a. 5bc (4b3c2) =*don’t forget about the hidden ones
b. 4a3mr (6am4) =*if a variable only appears once, keep it in the final answer
c. -2b3m4 (3b2m-2) =*don’t forget about integer rules!
d. 12a4bg3 (-2abg3) =
20b4c3
24a4m5r
-6b5m2
-24a5b2g6
![Page 13: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/13.jpg)
8.A.6 MULTIPLY MONOMIALS
Now You Try Some!
a) 4a3m (8a4m6)
b) 5c4a3 (-3c2a)
c) -6m4r-2 (3m0r6)
d) 2b6 (8b3c)
![Page 14: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/14.jpg)
8.A.6 MULTIPLY MONOMIALS
Now You Try Some!
a) 4a3m (8a4m6) = 32a7m7
b) 5c4a3 (-3c2a)
c) -6m4r-2 (3m0r6)
d) 2b6 (8b3c)
![Page 15: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/15.jpg)
8.A.6 MULTIPLY MONOMIALS
Now You Try Some!
a) 4a3m (8a4m6) = 32a7m7
b) 5c4a3 (-3c2a) = -15a4c6
c) -6m4r-2 (3m0r6)
d) 2b6 (8b3c)
![Page 16: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/16.jpg)
8.A.6 MULTIPLY MONOMIALS
Now You Try Some!
a) 4a3m (8a4m6) = 32a7m7
b) 5c4a3 (-3c2a) = -15a4c6
c) -6m4r-2 (3m0r6) = -18m4r4
d) 2b6 (8b3c)
![Page 17: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/17.jpg)
8.A.6 MULTIPLY MONOMIALS
Now You Try Some!
a) 4a3m (8a4m6) = 32a7m7
b) 5c4a3 (-3c2a) = -15a4c6
c) -6m4r-2 (3m0r6) = -18m4r4
d) 2b6 (8b3c) = 16b9c
![Page 18: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/18.jpg)
8.A.6 DIVIDE MONOMIALS
Just remember the quotient laws!
27a5b6 ÷ 9a2b
Quotient Law2 let’s us divide 27 by 9 = 3
Quotient Law1 lets us divide the variables
![Page 19: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/19.jpg)
8.A.6 DIVIDE MONOMIALS
Just remember the quotient laws!
27a5b6 ÷ 9a2b
Quotient Law2 let’s us divide 27 by 9 = 3
Quotient Law1 lets us divide the variables (which means subtract the exponents for each variable)
= 3a3b5
![Page 20: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/20.jpg)
8.A.6 DIVIDE MONOMIALS
Some Examples:
a)4a6b3 ÷ 2a3b
a)12m4n2 ÷ 4mn5
a)2a5b3 ÷ 3a3
b)5m7c4 ÷ 5m7c-9
![Page 21: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/21.jpg)
8.A.6 DIVIDE MONOMIALS
Some Examples:
a)4a6b3 ÷ 2a3b = 2a3b2
a)12m4n2 ÷ 4mn5
a)2a5b3 ÷ 3a3
b)5m7c4 ÷ 5m7c-9
![Page 22: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/22.jpg)
8.A.6 DIVIDE MONOMIALS
Some Examples:
a)4a6b3 ÷ 2a3b = 2a3b2
a)12m4n2 ÷ 4mn5 = 3m3n-3
a)2a5b3 ÷ 3a3
a)5m7c4 ÷ 5m7c-9
![Page 23: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/23.jpg)
8.A.6 DIVIDE MONOMIALS
Some Examples:
a)4a6b3 ÷ 2a3b = 2a3b2
a)12m4n2 ÷ 4mn5 = 3m3n-3
a)2a5b3 ÷ 3a3 = (2/3) a2b3
a)5m7c4 ÷ 5m7c-9
![Page 24: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/24.jpg)
8.A.6 DIVIDE MONOMIALS
Some Examples:
a)4a6b3 ÷ 2a3b = 2a3b2
a)12m4n2 ÷ 4mn5 = 3m3n-3
a)2a5b3 ÷ 3a3 = (2/3) a2b3
5m7c4 ÷ 5m7c-9 = 1m0c13
![Page 25: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/25.jpg)
8.A.6 DIVIDE MONOMIALS
Some Examples:
a)4a6b3 ÷ 2a3b = 2a3b2
a)12m4n2 ÷ 4mn5 = 3m3n-3
a)2a5b3 ÷ 3a3 = (2/3) a2b3
a)5m7c4 ÷ 5m7c-9 = 1m0c13 = c13
![Page 26: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/26.jpg)
8.A.6 DIVIDE MONOMIALS
Now You Try Some…Alone!
a) 30a6 ÷ 5a
a) 32b4m3 ÷ 8bm3
a) 16a7c3 ÷ 4a9
9b6r5 ÷ 6b2r-4
![Page 27: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/27.jpg)
8.A.6 DIVIDE MONOMIALS
Now You Try Some…Alone!
a) 30a6 ÷ 5a = 6a5
a) 32b4m3 ÷ 8bm3
a) 16a7c3 ÷ 4a9
9b6r5 ÷ 6b2r-4
![Page 28: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/28.jpg)
8.A.6 DIVIDE MONOMIALS
Now You Try Some…Alone!
a) 30a6 ÷ 5a = 6a5
a) 32b4m3 ÷ 8bm3 = 4b3m0
a) 16a7c3 ÷ 4a9
a) 9b6r5 ÷ 6b2r-4
![Page 29: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/29.jpg)
8.A.6 DIVIDE MONOMIALS
Now You Try Some…Alone!
a) 30a6 ÷ 5a = 6a5
a) 32b4m3 ÷ 8bm3 = 4b3m0 = 4b3
a) 16a7c3 ÷ 4a9
a) 9b6r5 ÷ 6b2r-4
![Page 30: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/30.jpg)
8.A.6 DIVIDE MONOMIALS
Now You Try Some…Alone!
a) 30a6 ÷ 5a = 6a5
a) 32b4m3 ÷ 8bm3 = 4b3m0 = 4b3
a) 16a7c3 ÷ 4a9 = 4a-2c3
a) 9b6r5 ÷ 6b2r-4
![Page 31: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/31.jpg)
8.A.6 DIVIDE MONOMIALS
Now You Try Some…Alone!
a) 30a6 ÷ 5a = 6a5
a) 32b4m3 ÷ 8bm3 = 4b3m0 = 4b3
a) 16a7c3 ÷ 4a9 = 4a-2c3
a) 9b6r5 ÷ 6b2r-4 = (3/2)b4r9
![Page 32: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/32.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL
This works a lot like Dividing a monomial by a monomial
15a4b7 + 6a2b4
3abBreak this into two separate fractions:
![Page 33: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/33.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL This works a lot like Dividing a monomial by a
monomial
15a4b7 + 6a2b4
3ab
Break this into two separate fractions:
![Page 34: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/34.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL This works a lot like Dividing a monomial by a
monomial
15a4b7 + 6a2b4
3ab
Break this into two separate fractions:
![Page 35: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/35.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL
15a4b7 + 6a2b4
3ab
Break this into two separate fractions:
15a4b7 = 6a2b4 =3ab 3ab
![Page 36: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/36.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL
15a4b7 + 6a2b4
3abNow follow Quotient Laws!
15a4b7 = 5a3b6 6a2b4 = 2ab3
3ab 3ab
![Page 37: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/37.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL
15a4b7 = 5a3b6 6a2b4 = 2ab3
3ab 3abPut these two parts together, using the
operation from the original! In this case, it was an addition problem, so the answer is…
5a3b6 + 2ab3
![Page 38: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/38.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL
One more example:
A. 18m6n9 − 24m4n7
6m2n3
![Page 39: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/39.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL
One more example:
A. 18m6n9 − 24m4n7
6m2n3
*break into two fractions!
18m6n9 = 24m4n7 = 6m2n3 6m2n3
![Page 40: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/40.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL
One more example:
A. 18m6n9 − 24m4n7
6m2n3
Follow quotient laws! 18m6n9 = 3m4n6 24m4n7 = 6m2n3 6m2n3
![Page 41: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/41.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL
One more example:
A. 18m6n9 − 24m4n7
6m2n3
Follow quotient laws
18m6n9 = 3m4n6 24m4n7 = 4m2n4 6m2n3 6m2n3
![Page 42: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/42.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL
One more example:
A. 18m6n9 − 24m4n7
6m2n3
*follow quotient laws!
18m6n9 = 3m4n6 24m4n7 = 4m2n4 6m2n3 6m2n3
*put it all together:
3m4n6 − 4m2n4
![Page 43: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/43.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL Now You Try Alone ! And don’t forget integer
rules!
A.30a6b2 − 27a4b6
3a3b4
B. 28m5n3p4 + 32m2n5p 4mn7p3
![Page 44: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/44.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL
Let’s Go Over Them!
A.30a6b2 − 27a4b6
3a3b4
30a6b2 = 27a4b6 = 3a3b4 3a3b4
![Page 45: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/45.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL
Let’s Go Over Them!
A.30a6b2 − 27a4b6
3a3b4
30a6b2 = 10a3b-2 27a4b6 = 3a3b4 3a3b4
![Page 46: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/46.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL
Let’s Go Over Them!
A.30a6b2 − 27a4b6
3a3b4
30a6b2 = 10a3b-2 27a4b6 = 9ab2
3a3b4 3a3b4
![Page 47: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/47.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL
Let’s Go Over Them!A. 30a6b2 − 27a4b6
3a3b4
30a6b2 = 10a3b-2 27a4b6 = 9ab2
3a3b4 3a3b
10a3b-2 − 9ab2
![Page 48: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/48.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL
Now You Try! And don’t forget integer rules!
B. 28m5n3p4 + 32m2n5p 4mn7p3
![Page 49: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/49.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL
Let’s Go Over Them!
B. 28m5n3p4 + 32m2n5p 4mn7p3
*Break into 2 fractions
28m5n3p4 32m2n5p
4mn7p3 4mn7p3
![Page 50: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/50.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL
Let’s Go Over Them!
B. 28m5n3p4 + 32m2n5p 4mn7p3
*Break into 2 fractions
28m5n3p4 = 7m4n-4p 32m2n5p =4mn7p3 4mn7p3
![Page 51: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/51.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL
Let’s Go Over Them!
B. 28m5n3p4 + 32m2n5p 4mn7p3
*Break into 2 fractions
28m5n3p4 = 7m4n-4p 32m2n5p = 8mn-2p-2
4mn7p3 4mn7p3
![Page 52: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/52.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL
Let’s Go Over Them!
B. 28m5n3p4 + 32m2n5p
4mn7p3
*Break into 2 fractions
28m5n3p4 = 7m4n-4p 32m2n5p = 8mn-2p-2
4mn7p3 4mn7p3
7m4n-4p + 8mn-2p-2
![Page 53: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/53.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL On loose leaf! On your own! Show the broken up
fractions!
1. 36a5b7 + 12a3b4
6ab4
2. 21c8d4 − 35c9d7c8d3
3. 40a6c5 + 60a2c7
20ac4
![Page 54: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/54.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL Let’s go over them…
1. 36a5b7 + 12a3b4 = 6a4b3 + 2a2
6ab4
2. 21c8d4 − 35c9d7c8d3
3. 40a6c5 + 60a2c7
20ac4
![Page 55: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/55.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL Let’s go over them…
1. 36a5b7 + 12a3b4 = 6a4b3 + 2a2
6ab4
2. 21c8d4 − 35c9d = 3d − 5cd-2 7c8d3
3. 40a6c5 + 60a2c7
20ac4
![Page 56: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/56.jpg)
8.A.9- DIVIDE A POLYNOMIAL BY A MONOMIAL Let’s go over them…
1. 36a5b7 + 12a3b4 = 6a4b3 + 2a2
6ab4
2. 21c8d4 − 35c9d = 3d − 5cd-2 7c8d3
3. 40a6c5 + 60a2c7 = 2a5c + 3ac3
20ac4
![Page 57: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/57.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A MONOMIAL
5(4 + 7) =
There are two ways to evaluate this equation. 1. PEMDAS
1. Distributive Property 5(4+7)
![Page 58: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/58.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A MONOMIAL
5(4 + 7) =
There are two ways to evaluate this equation. 1. PEMDAS Parentheses: 4+7 =11
1. Distributive Property 5(4+7)
![Page 59: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/59.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A MONOMIAL
5(4 + 7) =There are two ways to evaluate this equation. 1. PEMDAS Parentheses: 4+7 =11 Multiplication: 5(11) = 55
1. Distributive Property 5(4+7)
![Page 60: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/60.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A MONOMIAL
5(4 + 7) =There are two ways to evaluate this equation. 1. PEMDAS Parentheses: 4+7 =11 Multiplication: 5(11) = 55
1. Distributive Property 5(4+7) = 5(4) +
![Page 61: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/61.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A MONOMIAL
5(4 + 7) =There are two ways to evaluate this equation. 1. PEMDAS Parentheses: 4+7 =11 Multiplication: 5(11) = 55
1. Distributive Property 5(4+7) = 5(4) + 5(7)
![Page 62: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/62.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A MONOMIAL
5(4 + 7) =There are two ways to evaluate this equation. 1. PEMDAS Parentheses: 4+7 =11 Multiplication: 5(11) = 55
1. Distributive Property 5(4+7) = 5(4) + 5(7) = 20 + 35
![Page 63: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/63.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A MONOMIAL 5(4 + 7) =There are two ways to evaluate this equation. 1. PEMDAS Parentheses: 4+7 =11 Multiplication: 5(11) = 55
1. Distributive Property 5(4+7) = 5(4) + 5(7) = 20 + 35
= 55
![Page 64: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/64.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A MONOMIAL
Remember the Distributive Property (the milkman delivers to each house separately):
a(b + c) = ab +ac
5(c − 6d) =
-4a(7 + 6d) =
![Page 65: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/65.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A MONOMIAL
Remember the Distributive Property (the milkman delivers to each house separately):
a(b + c) = ab +ac
5(c − 6d) = 5c
-4a(7 + 6d) =
![Page 66: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/66.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A MONOMIAL
Remember the Distributive Property (the milkman delivers to each house separately):
a(b + c) = ab +ac
5(c − 6d) = 5c − 30dand these are not like terms, so this is the final answer!
-4a(7 + 6d) =
![Page 67: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/67.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A MONOMIAL
Remember the Distributive Property (the milkman delivers to each house separately):
a(b + c) = ab +ac
5(c − 6d) = 5c − 30dand these are not like terms, so this is the final answer!
-4a(7 + 6d) = -28a
![Page 68: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/68.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A MONOMIAL
Remember the Distributive Property (the milkman delivers to each house separately):
a(b + c) = ab +ac
5(c − 6d) = 5c − 30dand these are not like terms, so this is the final answer!
-4a(7 + 6d) = -28a − 24ad
![Page 69: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/69.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A MONOMIAL
Some Examples:
1.5z(a2 − 3b)
1.4r3(8r + 7)
1.6b2(7b + 3b)
![Page 70: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/70.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A MONOMIAL
Some Examples:
1.5z(a2 − 3b) = 5za2 − 15zb
1.4r3(8r + 7)
1.6b2(7b + 3b)
![Page 71: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/71.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A MONOMIAL
Some Examples:
1.5z(a2 − 3b) = 5za2 − 15zb
2.4r3(8r + 7) = 32r4 + 28r3 Don’t forget about product law! These aren’t like terms!!
1.6b2(7b + 3b)
![Page 72: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/72.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A MONOMIAL
Some Examples:
1.5z(a2 − 3b) = 5za2 − 15zb
2.4r3(8r + 7) = 32r4 + 28r3 Don’t forget about product law! These aren’t like terms!!
1.6b2(7b + 3b)= 42b3 + 18b3
![Page 73: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/73.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A MONOMIAL
Some Examples:
1.5z(a2 − 3b) = 5za2 − 15zb
2.4r3(8r + 7) = 32r4 + 28r3 Don’t forget about product law! These aren’t like terms!!
1.6b2(7b + 3b)= 42b3 + 18b3 = 60b3
These are like terms!
![Page 74: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/74.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A MONOMIAL
Now you try some… ALONE!
1. -4c(7 − 6d)
2. 8m(6m4 + m5)
3. -7a(4 − a)
4. 9b3 (7ab − 4ab4)
![Page 75: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/75.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A MONOMIAL
Now you try some… ALONE!
1. -4c(7 − 6d) = -28c + 24cd
2. 8m(6m4 + m5)
3. -7a(4 − a)
4. 9b3 (7ab − 4ab4)
![Page 76: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/76.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A MONOMIAL
Now you try some… ALONE!
1. -4c(7 − 6d) = -28c + 24cd *NB: a negative times a negative is a positive
1. 8m(6m4 + m5)
2. -7a(4 − a)
3. 9b3 (7ab − 4ab4)
![Page 77: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/77.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A MONOMIAL
Now you try some… ALONE!
1. -4c(7 − 6d) = -28c + 24cd *NB: a negative times a negative is a positive
8m(6m4 + m5) = 48m5 + 8m6
-7a(4 − a)
9b3 (7ab − 4ab4)
![Page 78: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/78.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A MONOMIAL
Now you try some… ALONE!
1. -4c(7 − 6d) = -28c + 24cd *NB: a negative times a negative is a positive
1. 8m(6m4 + m5) = 48m5 + 8m6
2. -7a(4 − a) = -28a +7a2
3. 9b3 (7ab − 4ab4)
![Page 79: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/79.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A MONOMIAL
Now you try some… ALONE!
1. -4c(7 − 6d) = -28c + 24cd *NB: a negative times a negative is a positive
1. 8m(6m4 + m5) = 48m5 + 8m6
2. -7a(4 − a) = -28a +7a2
3. 9b3 (7ab − 4ab4) = 63ab4 − 36ab7
![Page 80: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/80.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(n+4) (n−5)
For problems like this, we will learn about an important acronym : FOIL
Basically you use the distributive property twice.
![Page 81: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/81.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(n+4) (n−5)
![Page 82: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/82.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(n+4) (n−5)
F- firsts n n = n2
![Page 83: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/83.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(n+4) (n−5)
F- firsts n n = n2
O- outers n -5 = -5n
![Page 84: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/84.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(n+4) (n−5)
F- firsts n n = n2
O- outers n -5 = -5nI- inners 4 n = 4n
![Page 85: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/85.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(n+4) (n−5)
F- firsts n n = n2
O- outers n -5 = -5nI- inners 4 n = 4nL- lasts 4 -5 = -20
![Page 86: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/86.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(n+4) (n−5)
F- firsts n n = n2
O- outers n -5 = -5n like terms
I- inners 4 n = 4n = -nL- lasts 4 -5 = -20
![Page 87: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/87.jpg)
8.A.7 ADD AND SUBTRACT POLYNOMIALS
(n+4) (n−5)
F- firsts n n = n2
O- outers n -5 = -5n like termsI- inners 4 n = 4n = -nL- lasts 4 -5 = -20
So final answer: n2 − n − 20(the signs become the operators!)
![Page 88: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/88.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(a+2) (a+6)
![Page 89: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/89.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(a+2) (a+6)
F- firsts a a= a2
![Page 90: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/90.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(a+2) (a+6)
F- firsts a a = a2
O- outers a 6 = 6a
![Page 91: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/91.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(a+2) (a+6)
F- firsts a a = a2
O- outers a 6 = 6aI- inners 2 a = 2a
![Page 92: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/92.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(a+2) (a+6)
F- firsts a a = a2
O- outers a 6 = 6aI- inners 2 a = 2aL- lasts 2 6 = 12
![Page 93: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/93.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(a+2) (a+6)
F- firsts a a = a2
O- outers a 6 = 6a like terms
I- inners 2 a = 2a = 8aL- lasts 2 6 = 12
![Page 94: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/94.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(a+2) (a+6)
F- firsts a a = a2
O- outers a 6 = 6a like termsI- inners 2 a = 2a = 8aL- lasts 2 6 = 12
So final answer: a2 + 8a + 12(the signs become the operators!)
![Page 95: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/95.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
1. (a+3)(a−5)
2. (b−4)(b−3)
3. (c+6)(c−4)
4. (d−5)(d+5)
5. (3e+4)(2e−2)
![Page 96: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/96.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
1. (a+3)(a−5) = a2 − 2a − 15
2. (b−4)(b−3)
3. (c+6)(c−4)
4. (d−5)(d+5)
5. (3e+4)(2e−2)
![Page 97: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/97.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
1. (a+3)(a−5) = a2 − 2a − 15
2. (b−4)(b−3) = b2 − 7b + 12
3. (c+6)(c−4)
4. (d−5)(d+5)
5. (3e+4)(2e−2)
![Page 98: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/98.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
1. (a+3)(a−5) = a2 − 2a − 15
2. (b−4)(b−3) = b2 − 7b + 12
3. (c+6)(c−4) = c2 + 2c − 24
4. (d−5)(d+5)
5. (3e+4)(2e−2)
![Page 99: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/99.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
1. (a+3)(a−5) = a2 − 2a − 15
2. (b−4)(b−3) = b2 − 7b + 12
3. (c+6)(c−4) = c2 + 2c − 24
4. (d−5)(d+5) = d2 − 25
5. (3e+4)(2e−2)
![Page 100: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/100.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
1. (a+3)(a−5) = a2 − 2a − 15
2. (b−4)(b−3) = b2 − 7b + 12
3. (c+6)(c−4) = c2 + 2c − 24
4. (d−5)(d+5) = d2 − 25
5. (3e+4)(2e−2)= 6e2 +2e −8
![Page 101: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/101.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
Different Method- Area Model (n + 7)(n+3)
n + 7
n
+ 3
![Page 102: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/102.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
Different Method- Area Model (n + 7)(n+3)
n + 7
n
+ 3
n2
![Page 103: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/103.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
Different Method- Area Model (n + 7)(n+3)
n + 7
n
+ 3
n2 + 7n
![Page 104: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/104.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
Different Method- Area Model (n + 7)(n+3)
n + 7
n
+ 3
n2 + 7n
+3n
![Page 105: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/105.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
Different Method- Area Model (n + 7)(n+3)
n + 7
n
+ 3
n2 + 7n
+3n +21
![Page 106: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/106.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
Different Method- Area Model (n + 7)(n+3)
n + 7
n
+ 3
n2 + 7n
+3n +21
![Page 107: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/107.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
Different Method- Area Model (n + 7)(n+3)
n + 7
n
+ 3
n2 + 7n
+3n +21
![Page 108: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/108.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
Different Method- Area Model (n + 7)(n+3)
n + 7
n
+ 3
n2 + 10n + 21
n2 + 7n
+3n +21
![Page 109: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/109.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(a-5)(a+4) a -5
a
+ 4
![Page 110: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/110.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(a-5)(a+4) a -5
a
+ 4
a2
![Page 111: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/111.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(a-5)(a+4) a -5
a
+ 4
a2 -5a
![Page 112: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/112.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(a-5)(a+4) a -5
a
+ 4
a2 -5a
+4a
![Page 113: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/113.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(a-5)(a+4) a -5
a
+ 4
a2 -5a
+4a -20
![Page 114: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/114.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(a-5)(a+4) a -5
a
+ 4
a2 -5a
+4a -20
![Page 115: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/115.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(a-5)(a+4) a -5
a
+ 4
a2 -5a
+4a -20
![Page 116: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/116.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(a-5)(a+4) a -5
a
+ 4 a2 – 1a – 20
a2 -5a
+4a -20
![Page 117: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/117.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(a – 6)(a + 5)
(b + 4)(b – 8)
(c – 3)(4c + 5)
(3d – 6)(4d + 2)
![Page 118: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/118.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(a – 6)(a + 5) = a2 – 1a – 30
(b + 4)(b – 8)
(c – 3)(4c + 5)
(3d – 6)(4d + 2)
![Page 119: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/119.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(a – 6)(a + 5) = a2 – 1a – 30
(b + 4)(b – 8) = b2 – 4b – 32
(c – 3)(4c + 5)
(3d – 6)(4d + 2)
![Page 120: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/120.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(a – 6)(a + 5) = a2 – 1a – 30
(b + 4)(b – 8) = b2 – 4b – 32
(c – 3)(4c + 5) = 4c2 – 7c – 15
(3d – 6)(4d + 2)
![Page 121: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/121.jpg)
8.A.8- MULTIPLY A BINOMIAL BY A BINOMIAL
(a – 6)(a + 5) = a2 – 1a – 30
(b + 4)(b – 8) = b2 – 4b – 32
(c – 3)(4c + 5) = 4c2 – 7c – 15
(3d – 6)(4d + 2) = 12d2 – 18d – 12
![Page 122: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/122.jpg)
8.A.7 ADD AND SUBTRACT POLYNOMIALS
The main concept is Like Terms: matching variables (including their exponents)
LIKE: can be combined! Rules of exponents don’t come into play because you’re not x/÷. Leave variables as is!!
ax + 5ax
NON-LIKE
![Page 123: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/123.jpg)
8.A.7 ADD AND SUBTRACT POLYNOMIALS
The main concept is Like Terms: matching variables (including their exponents)
LIKE: can be combined! Rules of exponents don’t come into play because you’re not x/÷. Leave variables as is!!
ax + 5ax = 6ax 2b2 + 6b2
NON-LIKE
![Page 124: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/124.jpg)
8.A.7 ADD AND SUBTRACT POLYNOMIALS
The main concept is Like Terms: matching variables (including their exponents)
LIKE: can be combined! Rules of exponents don’t come into play because you’re not x/÷. Leave variables as is!!
ax + 5ax = 6ax 2b2 + 6b2 = 8b2
NON-LIKE
![Page 125: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/125.jpg)
8.A.7 ADD AND SUBTRACT POLYNOMIALS
The main concept is Like Terms: matching variables (including their exponents)
LIKE: can be combined! Rules of exponents don’t come into play because you’re not x/÷. Leave variables as is!!
ax + 5ax = 6ax 2b2 + 6b2 = 8b2
-3acd − 4acd
NON-LIKE
![Page 126: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/126.jpg)
8.A.7 ADD AND SUBTRACT POLYNOMIALS
The main concept is Like Terms: matching variables (including their exponents)
LIKE: can be combined! Rules of exponents don’t come into play because you’re not x/÷. Leave variables as is!!
ax + 5ax = 6ax 2b2 + 6b2 = 8b2
-3acd − 4acd = -7acd
NON-LIKE
![Page 127: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/127.jpg)
8.A.7 ADD AND SUBTRACT POLYNOMIALS The main concept is Like Terms: matching
variables (including their exponents) LIKE: can be combined! Rules of exponents don’t
come into play because you’re not x/÷. Leave variables as is!!
ax + 5ax = 6ax 2b2 + 6b2 = 8b2
-3acd − 4acd = -7acd
NON-LIKE: can’t be combined!
![Page 128: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/128.jpg)
8.A.7 ADD AND SUBTRACT POLYNOMIALS The main concept is Like Terms: matching variables
(including their exponents) LIKE: can be combined! Rules of exponents don’t
come into play because you’re not x/÷. Leave variables as is!!
ax + 5ax = 6ax 2b2 + 6b2 = 8b2
-3acd − 4acd = -7acd
NON-LIKE: can’t be combined!5x – 4y
![Page 129: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/129.jpg)
8.A.7 ADD AND SUBTRACT POLYNOMIALS The main concept is Like Terms: matching variables
(including their exponents) LIKE: can be combined! Rules of exponents don’t
come into play because you’re not x/÷. Leave variables as is!!
ax + 5ax = 6ax 2b2 + 6b2 = 8b2
-3acd − 4acd = -7acd
NON-LIKE: can’t be combined!5x – 4y 4a3 + 3a
![Page 130: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/130.jpg)
COMBINING LIKE TERMS
Always simplify to the minimum number of terms
Constants can be combined
![Page 131: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/131.jpg)
COMBINING LIKE TERMS
Always simplify to the minimum number of terms
Use the sign in front of the term as the operator Constants can be combined Examples:
1) 5x – 6 + 2x =
![Page 132: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/132.jpg)
COMBINING LIKE TERMS
Always simplify to the minimum number of terms
Use the sign in front of the term as the operator Constants can be combined Examples:
1) 5x – 6 + 2x = 7x – 6
![Page 133: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/133.jpg)
COMBINING LIKE TERMS Always simplify to the minimum number of
terms Use the sign in front of the term as the operator Constants can be combined Examples:
1) 5x – 6 + 2x = 7x – 6
2) -8 + 4g – 5 + 2g=
![Page 134: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/134.jpg)
COMBINING LIKE TERMS Always simplify to the minimum number of
terms Use the sign in front of the term as the operator Constants can be combined Examples:
1) 5x – 6 + 2x = 7x – 6
2) -8 + 4g – 5 + 2g= 6g – 13
![Page 135: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/135.jpg)
COMBINING LIKE TERMS Always simplify to the minimum number of
terms Use the sign in front of the term as the operator Constants can be combined Examples:
1) 5x – 6 + 2x = 7x – 6
2) -8 + 4g – 5 + 2g= 6g – 13
3) 3(5 + m) + 4 – 5m=
![Page 136: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/136.jpg)
COMBINING LIKE TERMS Always simplify to the minimum number of
terms Use the sign in front of the term as the operator Constants can be combined Examples:
1) 5x – 6 + 2x = 7x – 6
2) -8 + 4g – 5 + 2g= 6g – 13
3) 3(5 + m) + 4 – 5m= 15 + 3m + 4 – 5m =
![Page 137: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/137.jpg)
COMBINING LIKE TERMS Always simplify to the minimum number of
terms Use the sign in front of the term as the operator Constants can be combined Examples:
1) 5x – 6 + 2x = 7x – 6
2) -8 + 4g – 5 + 2g= 6g – 13
3) 3(5 + m) + 4 – 5m= 15 + 3m + 4 – 5m = 19 – 2m
![Page 138: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/138.jpg)
COMBINING LIKE TERMS
You Try Some: 1) 5a + 8 – 7a + 2
2) 3p – 3p + 2
3) 5h + 4h + 7h – 16h
4) 7 – 4a + 3a – 10
5) 4 – 2(b – 4) + 4b
![Page 139: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/139.jpg)
COMBINING LIKE TERMS
You Try Some: 1) 5a + 8 – 7a + 2 = -2a + 10
2) 3p – 3p + 2
3) 5h + 4h + 7h – 16h
4) 7 – 4a + 3a – 10
5) 4 – 2(b – 4) + 4b
![Page 140: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/140.jpg)
COMBINING LIKE TERMS
You Try Some: 1) 5a + 8 – 7a + 2 = -2a + 10
2) 3p – 3p + 2 = 0p + 2
3) 5h + 4h + 7h – 16h
4) 7 – 4a + 3a – 10
5) 4 – 2(b – 4) + 4b
![Page 141: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/141.jpg)
COMBINING LIKE TERMS
You Try Some: 1) 5a + 8 – 7a + 2 = -2a + 10
2) 3p – 3p + 2 = 0p + 2 = 2
3) 5h + 4h + 7h – 16h
4) 7 – 4a + 3a – 10
5) 4 – 2(b – 4) + 4b
![Page 142: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/142.jpg)
COMBINING LIKE TERMS
You Try Some: 1) 5a + 8 – 7a + 2 = -2a + 10
2) 3p – 3p + 2 = 0p + 2 = 2
3) 5h + 4h + 7h – 16h = 0h = 0
4) 7 – 4a + 3a – 10
5) 4 – 2(b – 4) + 4b
![Page 143: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/143.jpg)
COMBINING LIKE TERMS
You Try Some: 1) 5a + 8 – 7a + 2 = -2a + 10
2) 3p – 3p + 2 = 0p + 2 = 2
3) 5h + 4h + 7h – 16h = 0h = 0
4) 7 – 4a + 3a – 10 = -3 – 1a
5) 4 – 2(b – 4) + 4b
![Page 144: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/144.jpg)
COMBINING LIKE TERMS You Try Some: 1) 5a + 8 – 7a + 2 = -2a + 10
2) 3p – 3p + 2 = 0p + 2 = 2
3) 5h + 4h + 7h – 16h = 0h = 0
4) 7 – 4a + 3a – 10 = -3 – 1a
5) 4 – 2(b – 4) + 4b = 4 – 2b + 8 + 4b =
![Page 145: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/145.jpg)
COMBINING LIKE TERMS You Try Some: 1) 5a + 8 – 7a + 2 = -2a + 10
2) 3p – 3p + 2 = 0p + 2 = 2
3) 5h + 4h + 7h – 16h = 0h = 0
4) 7 – 4a + 3a – 10 = -3 – 1a
5) 4 – 2(b – 4) + 4b = 4 – 2b + 8 + 4b = 12 + 2b
![Page 146: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/146.jpg)
8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8a4 + 2a6) + (5a4 + 3a6)
(6b3 + 2b) + (5b − 4b3)
![Page 147: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/147.jpg)
8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8a4 + 2a6) + (5a4 + 3a6)+ 5a4 + 3a6
(6b3 + 2b) + (5b − 4b3)
![Page 148: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/148.jpg)
8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8a4 + 2a6) + (5a4 + 3a6)+ 5a4 + 3a6
(6b3 + 2b) + (5b − 4b3)
![Page 149: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/149.jpg)
8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8a4 + 2a6) + (5a4 + 3a6)+ 5a4 + 3a6
13a4 + 5a6
(6b3 + 2b) + (5b − 4b3)
![Page 150: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/150.jpg)
8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8a4 + 2a6) + (5a4 + 3a6)+ 5a4 + 3a6
13a4 + 5a6 This can’t be simplified further
(6b3 + 2b) + (5b − 4b3)
![Page 151: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/151.jpg)
8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8a4 + 2a6) + (5a4 + 3a6)+ 5a4 + 3a6
13a4 + 5a6 This can’t be simplified further
(6b3 + 2b) + (5b − 4b3)
![Page 152: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/152.jpg)
8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8a4 + 2a6) + (5a4 + 3a6)+ 5a4 + 3a6
13a4 + 5a6 This can’t be simplified further
(6b3 + 2b) + (5b − 4b3) −4b3 + 5b
![Page 153: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/153.jpg)
8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8a4 + 2a6) + (5a4 + 3a6)+ 5a4 + 3a6
13a4 + 5a6 This can’t be simplified further
(6b3 + 2b) + (5b − 4b3) −4b3 + 5b It switches to line up like terms
![Page 154: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/154.jpg)
8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8a4 + 2a6) + (5a4 + 3a6)+ 5a4 + 3a6
13a4 + 5a6 This can’t be simplified further
(6b3 + 2b) + (5b − 4b3) −4b3 + 5b It switches to line up like terms
2b3 + 7b
![Page 155: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/155.jpg)
8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8c5 + 3c) + (-5c5 + 6c2)
![Page 156: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/156.jpg)
8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8c5 + 3c) + (-5c5 + 6c2)
![Page 157: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/157.jpg)
8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8c5 + 3c) + (-5c5 + 6c2)
-5c5 + 6c2
![Page 158: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/158.jpg)
8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8c5 + 3c) + (-5c5 + 6c2)
-5c5 + 6c2
![Page 159: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/159.jpg)
8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8c5 + 3c) + (-5c5 + 6c2)
–5c5 + 6c2
![Page 160: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/160.jpg)
8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8c5 + 3c) + (-5c5 + 6c2)
–5c5 + 6c2
3c5 + 3c + 6c2
![Page 161: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/161.jpg)
8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(8c5 + 3c) + (-5c5 + 6c2)
–5c5 + 6c2 So if there’s no like term, leave 3c5 + 3c + 6c2 a gap
![Page 162: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/162.jpg)
8.A.7 ADD POLYNOMIALS
You Try!
1. (8a3 + 1a) + (6a + 7a3)
2. (6x2 + 11yz) + (8x2 – 9yz)
3. (3b4 – 2b2) + (6b4 + ba + 9b2)
![Page 163: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/163.jpg)
8.A.7 ADD POLYNOMIALS
You Try!
1. (8a3 + 1a) + (6a + 7a3)15a3 + 7a
2. (6x2 + 11yz) + (8x2 – 9yz)
3. (3b4 – 2b2) + (6b4 + ba + 9b2)
![Page 164: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/164.jpg)
8.A.7 ADD POLYNOMIALS
You Try!
1. (8a3 + 1a) + (6a + 7a3)15a3 + 7a
2. (6x2 + 11yz) + (8x2 – 9yz)14x2 + 2yz
3. (3b4 – 2b2) + (6b4 + ba + 9b2)
![Page 165: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/165.jpg)
8.A.7 ADD POLYNOMIALS
You Try!
1. (8a3 + 1a) + (6a + 7a3)15a3 + 7a
2. (6x2 + 11yz) + (8x2 – 9yz)14x2 + 2yz
3. (3b4 – 2b2) + (6b4 + ba + 9b2)9b4 + 7b2 + ba
![Page 166: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/166.jpg)
8.A.7 ADD POLYNOMIALS
Worksheet!
![Page 167: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/167.jpg)
![Page 168: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/168.jpg)
![Page 169: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/169.jpg)
8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(7c4 + 4c) + (5c3 + 2c)+ 2c + 5c3
7c4 + 6c + 5c3 be careful to line up like terms only!
(d3 – 4d2 + 5) + (2d3 +6d2 + 8d)
![Page 170: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/170.jpg)
8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(7c4 + 4c) + (5c3 + 2c)+ 2c + 5c3
7c4 + 6c + 5c3 be careful to line up like terms only!
(d3 – 4d2 + 5) + (2d3 +6d2 + 8d)
![Page 171: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/171.jpg)
8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(7c4 + 4c) + (5c3 + 2c)+ 2c + 5c3
7c4 + 6c + 5c3 be careful to line up like terms only!
(d3 – 4d2 + 5) + (2d3 +6d2 + 8d) +2d3 +6d2 +8d)
![Page 172: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/172.jpg)
8.A.7 ADD POLYNOMIALS
Line up like terms vertically!!
(7c4 + 4c) + (5c3 + 2c)+ 2c + 5c3
7c4 + 6c + 5c3 be careful to line up like terms only!
(d3 – 4d2 + 5) + (2d3 +6d2 + 8d) +2d3 +6d2 +8d) 3d3 + 2d2 +5 + 8d
![Page 173: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/173.jpg)
8.A.7 ADD POLYNOMIALS
You Try!1. (4x2y + 3y) + (8x2y +9y)
2. (5a3 + 10a) + (-4a3 + 6a)
3. (2b4 – 7b2) + (5b4 + 12ba + 9b2)
![Page 174: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/174.jpg)
8.A.7 SUBTRACT POLYNOMIALS
(8a2b + 5a) – (5a2b + 2a)Remember! K C CThe operator changes to addition and then all the signs of the
terms on the inside change !
(8a2b + 5a) – (5a2b + 2a)
![Page 175: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/175.jpg)
8.A.7 SUBTRACT POLYNOMIALS
(8a2b + 5a) – (5a2b + 2a)Remember! K C CThe operator changes to addition and then all the signs of the
terms on the inside change !
(8a2b + 5a) – (5a2b + 2a) +
![Page 176: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/176.jpg)
8.A.7 SUBTRACT POLYNOMIALS
(8a2b + 5a) – (5a2b + 2a)Remember! K C CThe operator changes to addition and then all the signs of the
terms on the inside change !
(8a2b + 5a) – (5a2b + 2a) + (-5a2b
![Page 177: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/177.jpg)
8.A.7 SUBTRACT POLYNOMIALS
(8a2b + 5a) – (5a2b + 2a)Remember! K C CThe operator changes to addition and then all the signs of the
terms on the inside change !
(8a2b + 5a) – (5a2b + 2a) + (-5a2b – 2a)
![Page 178: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/178.jpg)
8.A.7 SUBTRACT POLYNOMIALS
(8a2b + 5a) – (5a2b + 2a)Remember! K C CThe operator changes to addition and then all the signs of the
terms on the inside change !
(8a2b + 5a) – (5a2b + 2a) + (-5a2b – 2a)
![Page 179: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/179.jpg)
8.A.7 SUBTRACT POLYNOMIALS
(8a2b + 5a) – (5a2b + 2a)Remember! K C CThe operator changes to addition and then all the signs of the
terms on the inside change !
(8a2b + 5a) – (5a2b + 2a) + (-5a2b – 2a)
![Page 180: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/180.jpg)
8.A.7 SUBTRACT POLYNOMIALS
(8a2b + 5a) – (5a2b + 2a)Remember! K C CThe operator changes to addition and then all the signs of the
terms on the inside change !
(8a2b + 5a) – (5a2b + 2a) + (-5a2b – 2a) + (-5a2b – 2a)
![Page 181: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/181.jpg)
8.A.7 SUBTRACT POLYNOMIALS
(8a2b + 5a) – (5a2b + 2a)Remember! K C CThe operator changes to addition and then all the signs of the
terms on the inside change !
(8a2b + 5a) – (5a2b + 2a) + (-5a2b – 2a) + (-5a2b – 2a) 3a2b
![Page 182: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/182.jpg)
8.A.7 SUBTRACT POLYNOMIALS
(8a2b + 5a) – (5a2b + 2a)Remember! K C CThe operator changes to addition and then all the signs of the
terms on the inside change !
(8a2b + 5a) – (5a2b + 2a) + (-5a2b – 2a) + (-5a2b – 2a) 3a2b + 3a
![Page 183: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/183.jpg)
8.A.7 SUBTRACT POLYNOMIALS Another example!
(6b3 – 8bc) – (8b3 + 9bc)
![Page 184: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/184.jpg)
8.A.7 SUBTRACT POLYNOMIALS Another example!
(6b3 – 8bc) – (8b3 + 9bc) K C C
![Page 185: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/185.jpg)
8.A.7 SUBTRACT POLYNOMIALS Another example!
(6b3 – 8bc) – (8b3 + 9bc) K C C
+
![Page 186: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/186.jpg)
8.A.7 SUBTRACT POLYNOMIALS Another example!
(6b3 – 8bc) – (8b3 + 9bc) K C C
+ (-8b3
![Page 187: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/187.jpg)
8.A.7 SUBTRACT POLYNOMIALS Another example!
(6b3 – 8bc) – (8b3 + 9bc) K C C
+ (-8b3 – 9bc)
![Page 188: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/188.jpg)
8.A.7 SUBTRACT POLYNOMIALS Another example!
(6b3 – 8bc) – (8b3 + 9bc) K C C
+ (-8b3 – 9bc)
![Page 189: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/189.jpg)
8.A.7 SUBTRACT POLYNOMIALS Another example!
(6b3 – 8bc) – (8b3 + 9bc) K C C
+ (-8b3 – 9bc)
![Page 190: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/190.jpg)
8.A.7 SUBTRACT POLYNOMIALS Another example!
(6b3 – 8bc) – (8b3 + 9bc) K C C
+ (-8b3 – 9bc)+ (-8b3 – 9bc)
![Page 191: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/191.jpg)
8.A.7 SUBTRACT POLYNOMIALS Another example!
(6b3 – 8bc) – (8b3 + 9bc) K C C
+ (-8b3 – 9bc)+ (-8b3 – 9bc) -2b3
![Page 192: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/192.jpg)
8.A.7 SUBTRACT POLYNOMIALS Another example!
(6b3 – 8bc) – (8b3 + 9bc) K C C
+ (-8b3 – 9bc)+ (-8b3 – 9bc) -2b3 – 17bc
![Page 193: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/193.jpg)
8.A.7 SUBTRACT POLYNOMIALS
(15c3m – 4c2 + 8m) – (9c3m – 10m)
![Page 194: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/194.jpg)
8.A.7 SUBTRACT POLYNOMIALS
(15c3m – 4c2 + 8m) – (9c3m – 10m) K C C + (-9c3m +10m)
![Page 195: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/195.jpg)
8.A.7 SUBTRACT POLYNOMIALS
(15c3m – 4c2 + 8m) – (9c3m – 10m) K C C + (-9c3m +10m)
![Page 196: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/196.jpg)
8.A.7 SUBTRACT POLYNOMIALS
(15c3m – 4c2 + 8m) – (9c3m – 10m) K C C + (-9c3m +10m)
![Page 197: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/197.jpg)
8.A.7 SUBTRACT POLYNOMIALS
(15c3m – 4c2 + 8m) – (9c3m – 10m) K C C + (-9c3m +10m)
+ (-9c3m +10m) Remember to line up like terms!
6c3m – 4c2 + 18m
![Page 198: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/198.jpg)
8.A.7 SUBTRACT POLYNOMIALS You Try… On your own!(-5c3 – 4c4) – (2c3 + 5c4)
(5a3 + 7b) – (6b – 4a3)
(20v2 – 5m) – (12v2 – 4m + 2)
(8g4 + 6a – 7) – (5g4 – 10)
(9a2 – 5m) – (-6a2 + 8m)
![Page 199: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/199.jpg)
8.A.7 SUBTRACT POLYNOMIALS You Try… On your own!(-5c3 – 4c4) – (2c3 + 5c4)
-7c3 – 9c4
(5a3 + 7b) – (6b – 4a3)
(20v2 – 5m) – (12v2 – 4m + 2)
(8g4 + 6a – 7) – (5g4 – 10)
(9a2 – 5m) – (-6a2 + 8m)
![Page 200: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/200.jpg)
8.A.7 SUBTRACT POLYNOMIALS You Try… On your own! (-5c3 – 4c4) – (2c3 + 5c4)
-7c3 – 9c4
(5a3 + 7b) – (6b – 4a3)9a3 + b
(20v2 – 5m) – (12v2 – 4m + 2)
(8g4 + 6a – 7) – (5g4 – 10)
(9a2 – 5m) – (-6a2 + 8m)
![Page 201: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/201.jpg)
8.A.7 SUBTRACT POLYNOMIALS You Try… On your own! (-5c3 – 4c4) – (2c3 + 5c4)
-7c3 – 9c4
(5a3 + 7b) – (6b – 4a3)9a3 + b
(20v2 – 5m) – (12v2 – 4m + 2)8v2 – m – 2
(8g4 + 6a – 7) – (5g4 – 10)
(9a2 – 5m) – (-6a2 + 8m)
![Page 202: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/202.jpg)
8.A.7 SUBTRACT POLYNOMIALS You Try… On your own! (-5c3 – 4c4) – (2c3 + 5c4)
-7c3 – 9c4
(5a3 + 7b) – (6b – 4a3)9a3 + b
(20v2 – 5m) – (12v2 – 4m + 2)8v2 – m – 2
(8g4 + 6a – 7) – (5g4 – 10) 3g3 + 6a + 3
(9a2 – 5m) – (-6a2 + 8m)
![Page 203: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/203.jpg)
8.A.7 SUBTRACT POLYNOMIALS You Try… On your own! (-5c3 – 4c4) – (2c3 + 5c4)
-7c3 – 9c4
(5a3 + 7b) – (6b – 4a3)9a3 + b
(20v2 – 5m) – (12v2 – 4m + 2)8v2 – m – 2
(8g4 + 6a – 7) – (5g4 – 10) 3g3 + 6a + 3
(9a2 – 5m) – (-6a2 + 8m)15a2 – 13m
![Page 204: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/204.jpg)
8.A.7 ADD AND SUBTRACT POLYNOMIALS
1. (4a – 6a3) + (8a3 – 3a) 2. (7g + 2g2) – (7g2 + 2g)
3. (3m2 – 2m + 6) – (3m – 2m2)
4. (5c2 + 3c3) + (4c3 + 1)
5. (7x2 + 4) – (5 + 9x2)
6. (6n2 – 3n3) – (4n3 – 2n2 + 4n2)
![Page 205: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/205.jpg)
8.A.7 ADD AND SUBTRACT POLYNOMIALS
1. (4a – 6a3) + (8a3 – 3a) = a + 2a3
2. (7g + 2g2) – (7g2 + 2g)
3. (3m2 – 2m + 6) – (3m – 2m2)
4. (5c2 + 3c3) + (4c3 + 1)
5. (7x2 + 4) – (5 + 9x2)
6. (6n2 – 3n3) – (4n3 – 2n2 + 4n2)
![Page 206: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/206.jpg)
8.A.7 ADD AND SUBTRACT POLYNOMIALS
1. (4a – 6a3) + (8a3 – 3a) = a + 2a3
2. (7g + 2g2) – (7g2 + 2g) = 5g – 5g2
3. (3m2 – 2m + 6) – (3m – 2m2)
4. (5c2 + 3c3) + (4c3 + 1)
5. (7x2 + 4) – (5 + 9x2)
6. (6n2 – 3n3) – (4n3 – 2n2 + 4n2)
![Page 207: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/207.jpg)
8.A.7 ADD AND SUBTRACT POLYNOMIALS
1. (4a – 6a3) + (8a3 – 3a) = a + 2a3
2. (7g + 2g2) – (7g2 + 2g) = 5g – 5g2
3. (3m2 – 2m + 6) – (3m – 2m2) = 5m2 – 5m + 6
4. (5c2 + 3c3) + (4c3 + 1)
5. (7x2 + 4) – (5 + 9x2)
6. (6n2 – 3n3) – (4n3 – 2n2 + 4n2)
![Page 208: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/208.jpg)
8.A.7 ADD AND SUBTRACT POLYNOMIALS
1. (4a – 6a3) + (8a3 – 3a) = a + 2a3
2. (7g + 2g2) – (7g2 + 2g) = 5g – 5g2
3. (3m2 – 2m + 6) – (3m – 2m2) = 5m2 – 5m + 6
4. (5c2 + 3c3) + (4c3 + 1) = 7c3 + 5c2 + 1
5. (7x2 + 4) – (5 + 9x2)
6. (6n2 – 3n3) – (4n3 – 2n2 + 4n2)
![Page 209: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/209.jpg)
8.A.7 ADD AND SUBTRACT POLYNOMIALS
1. (4a – 6a3) + (8a3 – 3a) = a + 2a3
2. (7g + 2g2) – (7g2 + 2g) = 5g – 5g2
3. (3m2 – 2m + 6) – (3m – 2m2) = 5m2 – 5m + 6
4. (5c2 + 3c3) + (4c3 + 1) = 7c3 + 5c2 + 1
5. (7x2 + 4) – (5 + 9x2) = 2x2 – 1
6. (6n2 – 3n3) – (4n3 – 2n2 + 4n2)
![Page 210: Polynomials](https://reader036.fdocuments.in/reader036/viewer/2022062406/55a223a31a28ab747a8b46a3/html5/thumbnails/210.jpg)
8.A.7 ADD AND SUBTRACT POLYNOMIALS
1. (4a – 6a3) + (8a3 – 3a) = a + 2a3
2. (7g + 2g2) – (7g2 + 2g) = 5g – 5g2
3. (3m2 – 2m + 6) – (3m – 2m2) = 5m2 – 5m + 6
4. (5c2 + 3c3) + (4c3 + 1) = 7c3 + 5c2 + 1
5. (7x2 + 4) – (5 + 9x2) = 2x2 – 1
6. (6n2 – 3n3) – (4n3 – 2n2 + 4n2) = 4n2 – 7n3