Factorize the following
$(p - q)^{2} - 7 (p - q) - 18$

(p - q + 2) (p - q - 9)

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(p + q + 2) (p - q - 9)

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(p - q + 2) (p + q - 9)

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None of these

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Solution

The correct option is D $(p - q + 2) (p - q - 9)$
$(p - q)^{2} - 7 (p - q) - 18$
Let $p - q = t$
$- 9 + 2 = - 7$
$- 9 \times 2 = - 18$
$t^{2} - 7 t - 18$
$t^{2} + 2 t - 9 t - 18$
$t (t + 2) - 9 (t + 2)$
$(t + 2) (t - 9)$
$= (p - q + 2) (p - q - 9)$ Ans

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