Question

Factorize each of the following expression:
x − y − x² + y²

Answer 1

$$\begin{gathered} x-y-x^2+y^2 \\ =(x-y)+(y^2-x^2)[Regroupingtheterms] \\ =(x-y)+(y+x)(y-x) \\ =(x-y)-(y+x)(x-y)[\because (y-x)=-(x-y\left)\right] \\ =(x-y)[1-(y+x\left)\right] \\ =(x-y)(1-x-y) \end{gathered}$$