What will be the product of $p^{2} - 2 p q$ and $q^{2} + 5 p q$ ?

p q (4 p^{2} - 3 q^{2} + 11 p q)

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p q (4 p^{2} + 3 q^{2} + 11 p q)

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p q (5 p^{2} - 2 q^{2} - 9 p q)

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p q (4 p^{2} - 3 q^{2} - 11 p q)

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Solution

The correct option is C $p q (5 p^{2} - 2 q^{2} - 9 p q)$
$(p^{2} - 2 p q) \times (q^{2} + 5 p q)$

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

$= p^{2} q^{2} + 5 p^{3} q - 2 p q^{3} - 10 p^{2} q^{2}$

$= 5 p^{3} q - 2 p q^{3} + (p^{2} q^{2} - 10 p^{2} q^{2})$

$= 5 p^{3} q - 2 p q^{3} - 9 p^{2} q^{2}$

$= p q (5 p^{2} - 2 q^{2} - 9 p q)$

Suggest Corrections

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