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Question
Factorize each of the following expressions:
p2q − pr2 − pq + r2
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Solution
\[p^2 q - p r^2 - pq + r^2 \]
\[ = ( p^2 q - pq) + ( r^2 - p r^2 ) [\text{ Grouping the expressions }]\]
\[ = pq(p - 1) + r^2 (1 - p)\]
\[ = pq(p - 1) - r^2 (p - 1) [ \because (1 - p) = - (p - 1)]\]
\[ = (pq - r^2 )(p - 1) [\text{ Taking }(p - 1)\text{ as the common factor }]\]
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