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

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Solution

Given expression is $p^{2} q - p r^{2} - p q + r^{2}$
It can be written as $(p^{2} q - p r^{2} - p q + r^{2}) = p (p q - r^{2}) - 1 (p q - r^{2}) = (p - 1) (p q - r^{2})$
Thus factors are $(p - 1), (p q - r^{2})$ .

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