SIMPLIFYING ALGEBRAIC EXPRESSIONS
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SIMPLIFYING ALGEBRAIC EXPRESSIONS •ADDING LIKE TERMS •MULTIPLYING LIKE TERMS •SIMPLIFYING EXPRESSIONS •REPLACING LETTERS WITH NUMBERS TO GET A VALUE FOR AN EXPRESSION •USING FORMULAS •REMOVING BRACKETS
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SIMPLIFYING ALGEBRAIC EXPRESSIONS. ADDING LIKE TERMS. MULTIPLYING LIKE TERMS. SIMPLIFYING EXPRESSIONS. REPLACING LETTERS WITH NUMBERS TO GET A VALUE FOR AN EXPRESSION. USING FORMULAS. REMOVING BRACKETS. ADDING LIKE TERMS. 3 + 3 + 3 + 3. Can be written in the shorter form. - PowerPoint PPT Presentation
Transcript of SIMPLIFYING ALGEBRAIC EXPRESSIONS
SIMPLIFYING ALGEBRAIC EXPRESSIONS
•ADDING LIKE TERMS
•MULTIPLYING LIKE TERMS
•SIMPLIFYING EXPRESSIONS
•REPLACING LETTERS WITH NUMBERS TO GET A VALUE FOR AN EXPRESSION
•USING FORMULAS
•REMOVING BRACKETS
ADDING LIKE TERMS3 + 3 + 3 + 3 Can be written in the shorter form
4 X 3 Meaning that we have 4 bundles of 3’s
This gives the VALUE 12
a + a + a + a Can be written in the shorter form
4aWe cannot give a value for 4a until we are given a value for a
If a = 7 Then by replacing a with 7
4a = 4 x(7) = 28
So a value for the expression 4a when a = 7 is
28
3a + 2a = a+a+a + a+a
= 5a
Some examples
Simplify the following expressions
Combine all the a’s together to get one term
5b – 2b = b + b + b + b + b - b + b
= 3b Take 2 b’s away from the 5 b’s
Simplifying expressions with numbers and different letters
Simplify 3a + 2b + 5a + 3b + 7
3a + 5a 2b + 3b+
WE can only add or subtract like terms to each other
8a 5b+
8a + 5b +7
+ 7
+ 7
Multiplying like terms
2 X 2 X 2 X 2 X2 Can be written in the shorter form
25This means that 2 is multiplied by itself 5 times
This gives a value 32
a X a X a X a X a Can be written in the shorter form
a5We cannot get a value for a5 until we are given a value for a
If a = 7 then
a5 = 75
=16807
So a value for the expression a5
when a = 7 is 16807
Some examples
Simplify the following expressions
3a x a = 3 x a x a x a x aWe now have 3 times a multiplied by itself 4 times
= 3 a4
3b x 2b = 3 x 2 x b x b Multiply the numbers together and multiply the letters together= 6 x b2
Write product without multiplication sign
= 6 b2
3b2 X 4b3
3X4 b2X b3X
12 X bXb X bXbXb
12 X b5b2X b3 = b2+3 =b5
Multiply the numbers together
Add the powers
Examples with numbers and letters
Simplify
4r x 6s x r2 x s3
= 4 x 6 r x r2
=24 r3s4
When we multiply letters and numbers first put the numbers next the letters in alphabetical order and we do not need the X sign
Multiply the numbers together
Multiply similar letters together by adding the powers
s x s3
24 x r1+2 x
x x
s1+3
r = r1 REMEMBER
Order of operations
5 + 2 x 3 = 11 Not 21
In mathematics we have rules
Multiplication or division is calculated before addition or subtraction
2 x a + 5 Is simplified to 2a + 5
6 – 2 x bIs simplified to
6-2b
Have you got it yet ?
Simplify the following
1. 2a + 3a
2. 3a + 4b + 2a + 5b
3. b x b x b x b
4. b x b x c x c x c
5. 4b2 x 5b3
6. 3c x 4b
7. 2 c 4 + 3c4
8 . 3m + 2m + 7
9. 6j – 3j + j
10. 3s x 4s x 6
11. 3 x s + 7
12. 6 + 3 x d
13 . 10n – 2 x 3n
14. 8b – 3 x b2 .
5a
5a + 9b
b4
b2c3
20b5
12bc
5c4
5m+ 7
4j
72b2
3s+7
6+3d
4n
8b – 3 b2
Finding values for expressions
Find a value for the expression 3b when b =7
3b = 3 x (7) = 21
Take out b and replace it with 7
Put 7 inside a bracket
21 is the value of the expression
Find a value for the expression 3c + b when c = 2 and b = 5
3c + b
= 3 x (2) + ( 5)
= 6 + 5
= 11
Replace c with 2 and b with 5
11 is the value of the expression
Find a value for the expressions a) pq b) 2p + q c) 5pq +2p d) q2 - p2 when e) 3 ( p + 2q ) f) ( p + q ) 2 when p = 3 and q = 7
a) pq
= (3) x (7)
= 21
b) 2p + q
= 2 x ( 3) + ( 7 )
= 6 + 7
= 13
c) 3pq + 2p
= 3 x ( 3 ) x ( 7 ) + 2 x ( 3 )
= 63 + 6
= 69
d) q2 - p2
= (7)2 - (3)2
= 49 - 9
= 40
e) 3 ( p + 2q )
= 3 ( (7) + 2x(3) )
= 3( 7 + 6)
= 3 x 13 = 39
f) ( q - p ) 2
= ( (7) – (3) ) 2
= ( 4 ) 2
= 16
