Question

Factorise:
(x − 2y)² + 4x − 8y

Answer 1

We have:
$$\begin{gathered} {\left(x-2y\right)}^2+4x-8y={\left(x-2y\right)}^2+4\left(x-2y\right) \\ =\left(x-2y\right)\left(x-2y\right)+4\left(x-2y\right) \\ =\left(x-2y\right)\left\{\left(x-2y\right)+4\right\} \\ =\left(x-2y\right)\left(x-2y+4\right) \end{gathered}$$

∴ ${\left(x-2y\right)}^2+4x-8y=\left(x-2y\right)\left(x-2y+4\right)$