Question

Factorise:
x² − xz + xy − yz

Answer 1

By suitably arranging the terms:
$$\begin{gathered} x^2-xz+xy-yz=x^2+xy-xz-yz \\ =\left(x^2+xy\right)-\left(xz+yz\right) \\ =x\left(x+y\right)-z\left(x+y\right) \\ =\left(x+y\right)\left(x-z\right) \end{gathered}$$

∴ $x^2-xz+xy-yz=\left(x+y\right)\left(x-z\right)$