understanding the basics of expressions

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