Question

Factorise:
y² − xy(1 − x) − x³

Answer 1

We have:
$$\begin{gathered} y^2-xy\left(1-x\right)-x^3=y^2-xy+x^{2}y-x^3 \\ =\left(y^2-xy\right)+\left(x^{2}y-x^3\right) \\ =y\left(y-x\right)+x^2\left(y-x\right) \\ =\left(y-x\right)\left(y+x^2\right) \end{gathered}$$

∴ $y^2-xy\left(1-x\right)-x^3=\left(y-x\right)\left(y+x^2\right)$