Factorise:

Question:

Factorise:
y2 − xy(1 − x) − x3

Solution:

We have:

$y^{2}-x y(1-x)-x^{3}=y^{2}-x y+x^{2} y-x^{3}$

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

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

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

$\therefore y^{2}-x y(1-x)-x^{3}=(y-x)\left(y+x^{2}\right)$

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