Simplify :
${(a - b)}^{2} + 4 a b$

$a^{2}$ + $b^{2}$

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

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$a^{2}$ - $b^{2}$

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$a^{2} - b^{2} + 4 a b$

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Solution

The correct option is B
${(a + b)}^{2}$

$To Simplify : {(a - b)}^{2} + 4 a b$

Using the identity,
${(a - b)}^{2}$ = $a^{2} - 2 a b + b^{2}$

So,
${(a - b)}^{2} + 4 a b = a^{2} - 2 a b + b^{2} + 4 a b$
$= a^{2} + 2 a b + b^{2} = {(a + b)}^{2} ∵ (a + b)^{2} = a^{2} + 2 a b + b^{2}$

Hence,
${(a - b)}^{2} + 4 a b = {(a + b)}^{2}$

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