Cambridge International Mathematics

Algebra (Expansion and factorisation) (Chapter 1) 43

Example 17 Self Tutor

Fully factorise: a 3 a+6 b ab¡ 2 bc

3 a+6

= 3 £a+ 3 £ 2

=3(a+2) fHCF is 3 g

b ab¡ 2 bc

=a£b¡ 2 £b£c

=b(a¡ 2 c) fHCF isbg

Example 18 Self Tutor

Fully factorise: a 8 x^2 +12x b 3 y^2 ¡ 6 xy

a 8 x^2 +12x

=2£ 4 £x£x+3£ 4 £x

=4x(2x+3) fHCF is 4 xg

b 3 y^2 ¡ 6 xy

= 3 £y£y¡ 2 £ 3 £x£y

=3y(y¡ 2 x) fHCF is 3 yg

Example 19 Self Tutor

Fully factorise: a ¡ 2 a+6ab b ¡ 2 x^2 ¡ 4 x

a ¡ 2 a+6ab

=6ab¡ 2 a fWrite with 6 abfirst.g

= 2 £ 3 £a£b¡ 2 £a

=2a(3b¡1) fHCF is 2 ag

b ¡ 2 x^2 ¡ 4 x

=¡ 2 £x£x+¡ 2 £ 2 £x

=¡ 2 x(x+2) fHCF is ¡ 2 xg

Example 20 Self Tutor

Fully factorise:

a 2(x+3)+x(x+3) b x(x+4)¡(x+4)

a 2 (x+3)+x(x+3) fHCF is(x+3)g

=(x+ 3)(2 +x)

b x(x+4)¡(x+4) fHCF is(x+4)g

=x(x+4)¡1(x+4)

=(x+4)(x¡1)

Example 21 Self Tutor

Fully factorise (x¡1)(x+2)+3(x¡1)

(x¡1)(x+2)+3(x¡1) fHCF of(x¡1)g

=(x¡1)[(x+2)+3]

=(x¡1)(x+5)

With practice the

middle line is

not necessary.

Notice the use of

square brackets in the

second line. This helps

to distinguish between

the sets of brackets.

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Y:\HAESE\IGCSE01\IG01_01\043IGCSE01_01.CDR Thursday, 11 September 2008 9:10:54 AM PETER