Simplifying Polynomials 14-2 Warm Up Identify the coefficient of each monomial. 1. 3x 4 2. ab 3. 4....
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Transcript of Simplifying Polynomials 14-2 Warm Up Identify the coefficient of each monomial. 1. 3x 4 2. ab 3. 4....
Simplifying Polynomials14-2
Warm UpIdentify the coefficient of each monomial.
1. 3x4 2. ab
3. 4. –cb3
Use the Distributive Property to simplify each expression.
5. 9(6 + 7) 6. 4(10 – 2)
3 1
–1x2
12
117 32
Simplifying Polynomials14-2
Learn to simplify polynomials.
Simplifying Polynomials14-2
You can simplify a polynomial by adding or subtracting like terms. Remember that like terms have the same variables raised to the same powers.
4a3b2 + 3a2b3 – 2a3b2
Like terms
Not like terms
The variables have the same powers.
The variables have different powers.
Simplifying Polynomials14-2
Example 1: Identifying Like Terms
Identify the like terms in each polynomial.
A. 5x3 + y2 + 2 – 6y2 + 4x3
B. 3a3b2 + 3a2b3 + 2a3b2 - a3b2
Identify like terms. 5x + y + 2 – 6y + 4x3 2 2 3
Like terms: 5x3 and 4x3, y2 and –6y2
3a b + 3a b + 2a b – a b3 2 2 33 3 2 2 Identify like terms.
Like terms: 3a3b2, 2a3b2, and –a3b2
Simplifying Polynomials14-2
Example 1: Identifying Like Terms
Identify the like terms in the polynomial.
C. 7p3q2 + 7p2q3 + 7pq2
Identify like terms.
There are no like terms.
7p3q2 + 7p2q3 + 7pq2
Simplifying Polynomials14-2
Example 2
Identify the like terms in each polynomial.
A. 4y4 + y2 + 2 – 8y2 + 2y4
B. 7n4r2 + 3a2b3 + 5n4r2 + n4r2
Identify like terms. 4y + y + 2 – 8y + 2y4 2 2 4
Like terms: 4y4 and 2y4, y2 and –8y2
7n4r2 + 3a2b3 + 5n4r2 + n4r2 Identify like terms.
Like terms: 7n4r2, 5n4r2, and n4r2
Simplifying Polynomials14-2
Example 2
Identify the like terms in the polynomial.
C. 9m3n2 + 7m2n3 + pq2
Identify the like terms.
There are no like terms.
9m3n2 + 7m2n3 + pq2
Simplifying Polynomials14-2
To simplify a polynomial, combine like terms. It may be easier to arrange the terms in descending order (highest degree to lowest degree) before combining like terms.
Simplifying Polynomials14-2
Example 3A: Simplifying Polynomials by Combining Like Terms
Simplify.
4x2 + 2x2 + 7 – 6x + 9
Identify like terms. 4x2 + 2x2– 6x + 7 + 9
26x – 6x + 16 Combine coefficients: 4 + 2 = 6 and 7 + 9 = 16
Arrange in descending order.
4x2 + 2x2 – 6x + 7 + 9
Simplifying Polynomials14-2
Example 3B: Simplifying Polynomials by Combining Like Terms
Simplify.
3n5m4 – 6n3m + n5m4 – 8n3m
Arrange in descending order.
Identify like terms.
3n5m4 + n5m4 – 6n3m – 8n3m
Combine coefficients: 3 + 1 = 4 and –6 – 8 = –14.
3n5m4 + n5m4 – 6n3m – 8n3m
4n5m4 – 14n3m
Simplifying Polynomials14-2
Example 4A
Simplify.
2x3+ 5x3 + 6 – 4x + 9
Identify the like terms. Combine coefficients: 2 + 5 = 7 and 6 + 9 = 15
Arrange in descending order.
2x3+ 5x3 – 4x + 6 + 9
2x3+ 5x3 – 4x + 6 + 9
7x3 – 4x + 15
Simplifying Polynomials14-2
Example 4B
Simplify.
2n5p4 – 7n6p + n5p4 – 9n6p
Arrange in descending order.
Identify like terms.
Combine coefficients: 2 + 1 = 3 and –7 + –9 = –16
2n5p4 + n5p4 – 7n6p – 9n6p
2n5p4 + n5p4 – 7n6p – 9n6p
3n5p4 – 16n6p
Simplifying Polynomials14-2
Sometimes you may need to use the Distributive Property to simplify a polynomial.
Simplifying Polynomials14-2
Example 5A: Simplifying Polynomials by Using the Distributive Property
Simplify.
3(x3 + 5x2)
23(x + 5x )3 Distributive Property
3 x3 + 3 5x2
23x + 15x 3
Simplifying Polynomials14-2
Example 5B: Simplifying Polynomials by Using the Distributive Property
Simplify.
–4(3m3n + 7m2n) + m2n
Distributive Property –4(3m3n + 7m2n) + m2n
–4 3m3n – 4 7m2n + m2n
–12m3n – 28m2n + m2n
–12m3n – 27m2n Combine like terms.
Simplifying Polynomials14-2
Example 6A
Simplify.
2(x3 + 5x2)
2(x3+ 5x2) Distributive Property
2 x3 + 2 5x2
2x3 + 10x2
Simplifying Polynomials14-2
Example 6B
Simplify.
–2(6m3p + 8m2p) + m2p
Distributive Property –2(6m3p + 8m2p) + m2p
–2 6m3p – 2 8m2p + m2p
–12m3p – 16m2p + m2p
–12m3p – 15m2p Combine like terms.
Simplifying Polynomials14-2
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
Simplifying Polynomials14-2
Lesson Quiz
Identify the like terms in each polynomial.
1. 2x2 – 3z + 5x2 + z + 8z2
2. 2ab2 + 4a2b – 5ab2 – 4 + a2b
Simplify.
3. 5(3x2 + 2)
4. –2k2 + 10 + 8k2 + 8k – 2
5. 3(2mn2 + 3n) + 6mn2
2x and 5x , z and –3z2 2
2ab2 and –5ab2, 4a2b and a2b
15x2 + 10
6k2 + 8k + 8
12mn2 + 9n
Simplifying Polynomials14-2
1. Identify the like terms in the given polynomial. 3x3 – 7y +6x3 + y + 9y2
A. 3x3 and 6x3, –7y and 9y2
B. 3x3 and 9y2, y and –7y
C. 3x3 and 9y2, –7y and 9y2
D. 3x3 and 6x3, y and –7y
Lesson Quiz for Student Response Systems
Simplifying Polynomials14-2
2. Identify the like terms in the given polynomial. 4pq2 + 6p2q – 7pq2 – 11 + p2q
A. 4pq2 and –7pq2, 4pq2 and p2q
B. 4pq2 and –7pq2, 6p2q and p2q
C. 6p2q and –7pq2, 4pq2 and p2q
D. 6p2q and –7pq2, 6p2q and p2q
Lesson Quiz for Student Response Systems
Simplifying Polynomials14-2
3. Simplify. 7(4p2 + 3)
A. 11p2 + 21
B. 11p2 + 10
C. 28p2 + 10
D. 28p2 + 21
Lesson Quiz for Student Response Systems
Simplifying Polynomials14-2
4. Simplify. –5t2 + 7 + 11t2 + 9t – 4
A. 16t2 + 9t – 3
B. 6t2 + 16t – 4
C. 6t2 + 9t + 3
D. 16t2 + 9t + 11
Lesson Quiz for Student Response Systems