1. 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

2. ADDING LIKE TERMS 4 X 3 12 4a 3 + 3 + 3 + 3
Can be written in the shorter form
Meaning that we have 4 bundles of 3’s
4 X 3
This gives the VALUE 12
Can be written in the shorter form
a + a + a + a
We cannot give a value for 4a until we are given a value for a 4a

3. 28 If a = 7 Then by replacing a with 7 4a = 4 x(7) = 28
= 28
So a value for the expression 4a when a = is 28

4. Some examples
Simplify the following expressions
Combine all the a’s together to get one term
3a + 2a
= a+a+a a+a
= 5a
5b – 2b
= b + b + b + b + b
b + b
Take 2 b’s away from the 5 b’s
= 3b

5. Simplifying expressions with numbers and different letters
Simplify a + 2b + 5a + 3b + 7
WE can only add or subtract like terms to each other +
2b + 3b 7
3a + 5a + 5b 8a + 7 +
8a + 5b +7

6. Multiplying like terms
Can be written in the shorter form
2 X 2 X 2 X 2 X2
This means that 2 is multiplied by itself 5 times 25
This gives a value 32
a X a X a X a X a
Can be written in the shorter form
We cannot get a value for a5 until we are given a value for a a5

7. If a = 7 then a5
= 75
=16807
So a value for the expression a5 when a = is

8. Some examples
Simplify the following expressions
3a x a
= 3 x a x a x a x a
We 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
= x b2
Write product without multiplication sign
= 6 b2

9. Examples with numbers and letters
3b2 X 4b3
3X4 X
b2X b3 12 X
bXb X bXbXb
b2X b3 = b =b5 X 12 b5
Add the powers
Multiply the numbers together

10. Simplify
REMEMBER
r = r1
4r x 6s x r2 x s3
r x r2
= 4 x 6
s x s3 x x
Multiply similar letters together by adding the powers
Multiply the numbers together
s1+3 24 x
r1+2 x
When we multiply letters and numbers first put the numbers next the letters in alphabetical order and we do not need the X sign
=24 r3s4

11. Order of operations = Not 21 5 + 2 x 3 11 In mathematics we have rules
Multiplication or division is calculated before addition or subtraction
Is simplified to
2 x a + 5
2a + 5
Is simplified to
6 – 2 x b
6-2b

12. Have you got it yet ? Simplify the following 5a 5m+ 7 5a + 9b 4j b4
8 . 3m + 2m + 7
5m+ 7
1. 2a + 3a
9. 6j – 3j + j
5a + 9b 4j
2. 3a + 4b + 2a + 5b
3. b x b x b x b b4
10. 3s x 4s x 6
72b2
4. b x b x c x c x c
x s + 7
3s+7
b2c3
20b5
6+3d
5. 4b2 x 5b3
x d
n – 2 x 3n 4n
12bc
6. 3c x 4b .
5c4
14. 8b – 3 x b2
8b – 3 b2
7. 2 c c4

13. Finding values for expressions
Find a value for the expression 3b when b =7
3b =
3 x (7)
= 21
21 is the value of the expression
Take out b and replace it with 7
Put 7 inside a bracket

14. Find a value for the expression 3c + b when c = 2 and b = 5
Replace c with 2 and b with 5
= 3 x (2) + ( 5) =
= 11
11 is the value of the expression

15. Find a value for the expressions a) pq b) 2p + q c) 5pq +2p d) q p2 when e) 3 ( p + 2q ) f) ( p + q ) when p = 3 and q = 7
a) pq
b) 2p + q
c) 3pq + 2p
= 3 x ( 3 ) x ( 7 ) + 2 x ( 3 )
= (3) x (7)
= 2 x ( 3) + ( 7 ) = =
= 21
= 13
= 69
q p2 d)
e) 3 ( p + 2q )
f) ( q - p ) 2
= (7) (3)2
= 3 ( (7) + 2x(3) )
= ( (7) – (3) ) 2 =
= 3( )
= ( 4 ) 2
= 40 39
= 3 x 13 =
= 16