Factorize each of the following expression:
$p^{2} q - p r^{2} - p q + r^{2}$

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Solution

Given: $p^{2} q - p r^{2} - p q + r^{2}$

$∴ p^{2} q - p r^{2} - p q + r^{2}$
$= p^{2} q - p q - p r^{2} + r^{2}$
$= p q (p - 1) + r^{2} (- p + 1)$
$= p q (p - 1) - r^{2} (p - 1)$
$= (p - 1) (p q - r^{2})$

Hence, $p^{2} q - p r^{2} - p q + r^{2} = (p - 1) (p q - r^{2})$

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p^{2} q - p r^{2} - p q + r^{2}

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p^{2} + q^{2} + r^{2} + 2 p q + 2 q r + 2 r p

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