Question
Factor polynomial $$ p^{2}q-pr^{2}-pq+r^{2} $$
Answer
$$ p^{2}q-pr^{2}-pq+r^{2} = (p-1)(pq-r^{2}) $$
Explanation
To factor $ p^2q-pr^2-pq+r^2 $ we can use factoring by grouping.
Group $ \color{blue}{ p^2q }$ with $ \color{blue}{ -pr^2 }$ and $ \color{red}{ -pq }$ with $ \color{red}{ r^2 }$ then factor each group.
$$ \begin{aligned} p^2q-pr^2-pq+r^2 &= ( \color{blue}{ p^2q-pr^2 } ) + ( \color{red}{ -pq+r^2 }) = \\ &= \color{blue}{ p( pq-r^2 )} \color{red}{ -1( pq-r^2 ) } = \\ &= (p-1)(pq-r^2) \end{aligned} $$This page was created using
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