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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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