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10.4
Factorisation
This section will show you how to:
● ‘reverse’ the process of expanding brackets by
taking out a common factor from each term in
an expression
Key words
factor
factorisation
Factorisation is the opposite of expansion. It puts an expression into brackets.
To factorise an expression, look for the common factors in every term of the expression. Follow
through the examples below to see how this works.
EXAMPLE 12
Factorise each expression. a 6t + 9m
c 8kp + 4k – 12km
b 6my + 4py
d 8kp + 4kt – 12km
a The common factor is 3, so 6t + 9m = 3(2t + 3m)
b The common factor is 2y, so 6my + 4py = 2y(3m + 2p)
c The common factor is 4k, so 8kp + 4k – 12km = 4k(2p + 1 – 3m)
d The common factor is 4k, so 8kp + 4kt – 12km = 4k(2p + t – 3m)
Notice that if you multiply out each answer you will get the expressions
you started with.
This diagram may help you to see the difference and the
connection between expansion and factorisation.
Note: When the whole term is the common factor, as in
part c, then you are left with 1, not 0, inside the brackets.
Expanding
3(2t + 3m) = 6t + 9m
F a ct o r i s i n g
EXERCISE 10F
D
Factorise the following expressions. The first three have been started for you.
a
6m + 12t = 6( )
b
9t + 3p = 3( )
c
8m + 12k = 4( )
2
d
4r + 8t
e
mn + 3m
f
5g + 3g
g
4w – 6t
h
8p – 6k
i
16h – 10k
j
2mp + 2mk
k
4bc + 2bk
l
6ab + 4ac
o
4d 2 – 2d
2
m
3y + 2y
p
3m2 – 3mp
n
2
4t – 3t
First look for a common
factor of the numbers and
then look for common
factors of the letters.
UNIT 2 323