Question

1.2 factorisation by grouping terms

1. factorise the following.

(a) $5x(2p + 3q) + 4y(2p + 3q)$
(b) $9a(4x - 7y) - b(4x - 7y)$

1. factorise the following.

(a) $3m + 6n + 18mt + 36nt$
(b) $au - 5b + ab - 5u$
hint: rearrange terms if no common factors
if both terms have a negative sign, we extract the negative sign too

Explanation:

1(a) Step1: Identify common binomial factor

Common factor: $(2p+3q)$

1(a) Step2: Factor out the common term

$5x(2p+3q)+4y(2p+3q)=(2p+3q)(5x+4y)$

1(b) Step1: Identify common binomial factor

Common factor: $(4x-7y)$

1(b) Step2: Factor out the common term

$9a(4x-7y)-b(4x-7y)=(4x-7y)(9a-b)$

2(a) Step1: Group terms with common factors

$(3m+6n)+(18mt+36nt)$

2(a) Step2: Factor out GCF from each group

$3(m+2n)+18t(m+2n)$

2(a) Step3: Factor out common binomial factor

$3(m+2n)(1+6t)$

2(b) Step1: Rearrange terms to group

$(au-5u)+(ab-5b)$

2(b) Step2: Factor out GCF from each group

$u(a-5)+b(a-5)$

2(b) Step3: Factor out common binomial factor

$(u+b)(a-5)$

Answer:

1. (a) $\boldsymbol{(2p+3q)(5x+4y)}$
2. (b) $\boldsymbol{(4x-7y)(9a-b)}$
3. (a) $\boldsymbol{3(1+6t)(m+2n)}$
4. (b) $\boldsymbol{(u+b)(a-5)}$