Evaluate ${(4 a + 3 b)}^{2} - {(4 a - 3 b)}^{2} + 48 a b$

96 a

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96 a b

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45 b

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26 a b

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Solution

The correct option is B $96 a b$
${(4 a + 3 b)}^{2} - {(4 a - 3 b)}^{2} + 48 a b$
Using,
$(a - b)^{2} = (a^{2} - 2 a b + b^{2})$ and $(a + b)^{2} = (a^{2} + 2 a b + b^{2})$
$= [(4 a)^{2} + 2 (4 a) (3 b) + (3 b)^{2}] - [(4 a)^{2} - 2 (4 a) (3 b) + (3 b)^{2}] + 48 a b$
$= 16 a^{2} + 24 a b + 9 b^{2} - 16 a^{2} + 24 a b - 9 b^{2} + 48 a b$
$= 96 a b$

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