4.5Factorisation

Factorisation is the reverse of expansion. Instead of distributing a factor into a bracket, we extract a common factor out of the terms.

Factorisation

ab + ac = a(b + c)

Factorise $\displaystyle 15y - 21$ completely.

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HCF of

15

and

21

3

15y - 21 = 3(5y - 7)

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Factorise $10x - 4$ .

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HCF of

10

and

4

2

10x - 4 = 2(5x - 2)

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Factorise $\displaystyle 12mn^2 - 8m^2n$ completely.

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Common factors: HCF of

12

and

8

4

; both terms contain

m

and

n

HCF

= 4mn

12mn^2 - 8m^2n = 4mn(3n - 2m)

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Factorise $-10x + 10y$ .

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Take out

-10

as a common factor:

-10x + 10y = -10(x - y)

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(a) Factorise $\displaystyle 8a^2 + 12a$ completely. (b) Hence evaluate $\displaystyle 8a^2 + 12a$ when $\displaystyle a = 50$ .

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(a) HCF of

8

and

12

4

; both terms contain

a

, so the HCF is

4a

\displaystyle 8a^2 + 12a

\displaystyle = 4a(2a + 3)

(b) Substitute

a = 50

\displaystyle 4a(2a + 3)

\displaystyle = 200 \times 103

\displaystyle = 20\,600

The factorised form turns the sum into one easy product.