Which of the following is the expression obtained by the division of $5 p q (p^{2} - q^{2})$ by $2 p (p + q) ?$

$\frac{5 q (p - q)}{4}$

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$\frac{5 q (p + q)}{2}$

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$\frac{5 q (p - q)}{2}$

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$\frac{5 q (p + q)}{4}$

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Solution

The correct option is C
$\frac{5 q (p - q)}{2}$

Given, the expression is
$5 p q (p^{2} - q^{2}) .$

$[Using the identity: a^{2} - b^{2} = (a + b) (a - b)]$

$\Rightarrow 5 p q (p^{2} - q^{2}) = 5 p q (p + q) (p - q)$

Now dividing the above expression by
$2 p (p + q), we get$

$\frac{5 p q (p + q) (p - q)}{2 p (p + q)}$

$= \frac{5 q (p - q)}{2}$

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p^{2}

q^{2}

When $5 p q (p^{2} - q^{2})$ is divided by $2 p (p + q)$ and substituting $p = 3$ , $q = 1$ the value obtained is _______ .