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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Similar questions

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 _______ .

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:

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

5 p q (p^{2} - q^{2}) \div 2 p (p + q)

5 p q (p^{2} - q^{2}) \div 2 p (p + q)

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