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The standard identity ${(a + b)}^{2}$ is equal to ______.

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

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

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

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

answer is A.

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Detailed Solution

Consider the product, $(a + b) (a + b)$ .

$(a + b) (a + b) = a (a + b) + b (a + b)$

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

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

Therefore, ${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$ .

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