Question

Factorise $x(x-y{)}^3+3x^{2}y(x-y)$

Answer 1

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