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

$48 p q^{2}$

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$48 p^{2} q$

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$44 p^{2} q$

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$44 p q^{2}$

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Solution

The correct option is A
$48 p q^{2}$

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

We have:

$(a + b)^{2} = a^{2} + 2 a b + b^{2} (a - b)^{2} = a^{2} - 2 a b + b^{2}$

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

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

$= 24 p q^{2} + 24 p q^{2}$
$= 48 p q^{2}$

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

Prove that: $(4 p q + 3 q)^{2} - (4 p q - 3 q)^{2} = 48 p q^{2}$ .

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

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