Question

Factorize each of the following expressions:
p²q − pr² − pq + r²

Answer 1

$$\begin{gathered} p^{2}q-p{r}^2-pq+r^2 \\ =(p^{2}q-pq)+(r^2-p{r}^2)[Groupingtheexpressions] \\ =pq(p-1)+r^2(1-p) \\ =pq(p-1)-r^2(p-1)[\because (1-p)=-(p-1\left)\right] \\ =(pq-r^2)(p-1)[Taking(p-1)asthecommonfactor] \end{gathered}$$