Factorize the polynomial, $- r^{2} + p^{2} + q^{2} - 2 p q$ .

(p - q - r) (p - q + r)

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(p + q + r) (p - q - r)

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(p - q) (q - r)

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(p - r) (q - r)

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Solution

The correct option is A $(p - q - r) (p - q + r)$
Given polynomial,

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

$= (p - q)^{2} - r^{2}$ $[∵ (a - b)^{2} = a^{2} + b^{2} - 2 a b]$

$= (p - q - r) (p - q + r) .$ $[∵ (a^{2} - b^{2}) = (a - b) (a + b)]$

Hence, this is the answer.

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