This document discusses simplifying algebraic expressions through combining like terms, multiplying like terms, and evaluating expressions by substituting values for variables. It covers adding, subtracting, multiplying, and dividing terms. Examples are provided to demonstrate simplifying expressions with numbers and variables as well as evaluating expressions by replacing variables with values. Order of operations and dividing terms are also explained.

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
3 + 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
4a
We cannot give a value for 4a until we
are given a value for a

3. 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

4. 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

5. 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

6. Multiplying like terms
2 X 2 X 2 X 2 X2
Can be written in the shorter form
25
This 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
a5
We cannot get a value for a5
until
we are given a value for a

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

8. Some examples
Simplify the following expressions
3a3
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= 6 x b2
Write product
without
multiplication sign
= 6 b2

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

10. Simplify
4r x 6s x r2
x s3
= 4 x 6 r x r2
=24 r3
s4
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

11. 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 b
Is simplified to
6-2b

12. 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
b2
c3
20b5
12bc
5c4
5m+ 7
4j
72b2
3s+7
6+3d
4n
8b – 3 b2

13. Dividing terms
Remember, in algebra we do not usually use the division sign, ÷.
Instead we write the number or term we are dividing by
underneath like a fraction.
For example,
(a + b) ÷ c is written as a + b
c

14. Like a fraction, we can often simplify expressions by cancelling.
For example,
n3
÷ n2
=
n3
n2
=
n × n × n
n × n
1
1
1
1
= n
6p2
÷ 3p =
6p2
3p
=
6 × p × p
3 × p
2
1
1
1
= 2p
Dividing terms

15. Write Algebraic Expressions
for These Word Phrases
Ten more than a number
A number decrease by 5
6 less than a number
A number increased by 8
The sum of a number & 9
4 more than a number
n + 10
w - 5
x - 6
n + 8
n + 9
y + 4

16. Write Algebraic Expressions
for These Word Phrases
A number s plus 2
A number decrease by 1
31 less than a number
A number b increased by
7
The sum of a number & 6
9 more than a number
s + 2
k - 1
x - 31
b + 7
n + 6
z + 9

17. 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

18. Evaluate each algebraic
expression when x = 10
x + 8
x + 49
x + x
x - x
x - 7
42 - x
18
59
20
0
3
32

19. 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
Extended activity

20. 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