Question:
Factorize each of the following expressions:
qr − pr + qs − ps
Solution:
$p^{2} q-p r^{2}-p q+r^{2}$
$=\left(p^{2} q-p q\right)+\left(r^{2}-p r^{2}\right) \quad[$ Grouping the expressions $]$
$=p q(p-1)+r^{2}(1-p)$
$=p q(p-1)-r^{2}(p-1)$ $[\because(1-p)=-(p-1)]$
$=\left(p q-r^{2}\right)(p-1)$ $[$ Taking $(p-1)$ as the common factor $]$
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