What will be the product of $p^{2} - 3 p q$ and $q^{2} + 4 p q$ ?

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 (- 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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Solution

The correct option is B $p q (4 p^{2} - 3 q^{2} - 11 p q)$
Product of $p^{2} - 3 p q$ and $q^{2} + 4 p q$

$= (p^{2} - 3 p q) \times (q^{2} + 4 p q)$

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

$= p^{2} q^{2} + 4 p^{3} q - 3 p q^{3} - 12 p^{2} q^{2}$

$= 4 p^{3} q - 3 p q^{3} + (p^{2} q^{2} - 12 p^{2} q^{2})$

$= 4 p^{3} q - 3 p q^{3} - 11 p^{2} q^{2}$

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

The correct option is B.

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Question 59 (b)

What should be added to $3 p q + 5 p^{2} q^{2} + p^{3}$ to get $p^{3} + 2 p^{2} q^{2} + 4 p q ?$

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