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

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Solution

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

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

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

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

$= - 2 b (b + a)$

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