Question

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

Answer 1

\[p^2 q - p r^2 - pq + r^2 \]
\[ = ( p^2 q - pq) + ( r^2 - p r^2 ) [\text{ Grouping the expressions }]\]
\[ = pq(p - 1) + r^2 (1 - p)\]
\[ = pq(p - 1) - r^2 (p - 1) [ \because (1 - p) = - (p - 1)]\]
\[ = (pq - r^2 )(p - 1) [\text{ Taking }(p - 1)\text{ as the common factor }]\]