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The standard identity $(a - b) (a + b)$ is equal to ______.

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

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

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

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

answer is A.

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Detailed Solution

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

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

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

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

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

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