$1 - 2 a b - (a^{2} + b^{2}) = ? (a) (1 + a - b) (1 + a + b) (b) (1 + a + b) (1 - a + b) (c) (1 + a + b) (1 - a - b) (d) (1 + a - b) (1 - a + b)$

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Solution

$1 - 2 a b - (a^{2} + b^{2}) = 1 - 2 a b - a^{2} - b^{2} = 1 - (a^{2} + b^{2} + 2 a b) = 1 - (a + b)^{2} = (1 + a + b) (1 - a - b)$

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