What is the expansion for the identity ${(a - b)}^{2}$ ?

a^{2} - b^{2}

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

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(a^{2} - b^{2} - 2 a b)

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

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Solution

The correct option is D $(a^{2} + b^{2} - 2 a b)$
${(a - b)}^{2} = (a - b) (a - b)$
$= a (a - b) - b (a - b)$
$= a^{2} - a b - a b + b^{2}$
$= a^{2} - 2 a b + b^{2}$
$= a^{2} + b^{2} - 2 a b$

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