Question

Factorise:
$4(x-y{)}^2-12(x-y\left)\right(x+y)+9(x+y{)}^2$
.........[3 marks]

Answer 1

Let $(x–y)=p,(x+y)=q$, so we get:

$4p^2-12pq+9q^2$

Factorising the middle term:
$-12=-6,-6$, also $4\times 9=-6\times -6$

Now we have
$=4p^2-6pq-6pq+9q^2$

$=2p(2p-3q)-3q(2p-3q)$

$=(2p–3q)(2p–3q)$

$=(2p-3q{)}^2$.........[1 mark]

Substituting $p=x–y$, and $q=x+y$;

$=\left[2\right(x-y)-3(x+y){]}^2$

$=[2x-2y-3x-3y{]}^2$

$=(-x-5y{)}^2$

$=\left[\right(-1\left)\right(x+5y){]}^2$

$=(x+5y{)}^2$
..........[2 marks]