Add: $p (p - q), q (q - r) a n d r (r - p)$ .

p^{3} + q^{2} - r^{2} - p q - q - p r

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p^{2} - q^{2} + r^{3} - p q - q r - p r

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p^{2} 3 + q^{2} + r^{3} - p q - q r - p r

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

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Solution

The correct option is D $p^{2} + q^{2} + r^{2} - p q - q r - p r$
$p (p - q), q (q - r), r (r - p)$

$\Rightarrow$ $(p^{2} - p q), (q^{2} - q r), (r^{2} - p r)$
Adding we get,
$= (p^{2} - p q) + (q^{2} - q r) + (r^{2} - p r)$

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

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