Question

Factorise:
ab² − bc² − ab + c²

Answer 1

By suitably arranging the terms:
$$\begin{gathered} a{b}^2-b{c}^2-ab+c^2=a{b}^2-ab-b{c}^2+c^2 \\ =\left(a{b}^2-ab\right)-\left(b{c}^2-c^2\right) \\ =ab\left(b-1\right)-c^2\left(b-1\right) \\ =\left(b-1\right)\left(ab-c^2\right) \end{gathered}$$

∴ $a{b}^2-b{c}^2-ab+c^2=\left(b-1\right)\left(ab-c^2\right)$