Question: Factorise:
y2 − xy(1 − x) − x3
Solution:
We have:
$y^{2}-x y(1-x)-x^{3}=y^{2}-x y+x^{2} y-x^{3}$
$=\left(y^{2}-x y\right)+\left(x^{2} y-x^{3}\right)$
$=y(y-x)+x^{2}(y-x)$
$=(y-x)\left(y+x^{2}\right)$
$\therefore y^{2}-x y(1-x)-x^{3}=(y-x)\left(y+x^{2}\right)$
