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${(p + q)}^{2} - 20 (p + q) - 125$

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Solution

${(p + q)}^{2} - 20 (p + q) - 125$

Let $t = p + q$

$= t^{2} - 20 t - 125$

$= t^{2} - 25 t + 5 t - 125$

$= t (t - 25) + 5 (t - 25)$

$= (t + 5) (t - 25)$

$= (p + q + 5) (p + q - 25)$ where $t = p + q$

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