Factorize the following expressions
$p^{2} + q^{2} + r^{2} + 2 p q + 2 q r + 2 r p$

(p + q + r)^{2}

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(p + q - r)^{2}

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(p + q + r)^{3}

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None of these

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Solution

The correct option is B $(p + q + r)^{2}$
$(p + q)^{2} + r^{2} + 2 r (p + q)$

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

Using $(a + b)^{2} = a^{2} + b^{2} + 2 a b$ , where $a = (p + q)$ and $b = r$

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

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