Factorise :

$1 - 2 a - 2 b - 3 (a + b)^{2}$

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Solution

$1 - 2 a - 2 b - 3 (a + b)^{2} = 1 - 2 (a + b) - 3 (a + b)^{2} = 1 - 3 (a + b) + (a + b) - 3 (a + b)^{2} = [1 - 3 (a + b)] + (a + b) [1 - 3 (a + b)] = [1 - 3 (a + b)] (1 + a + b) = (1 - 3 a - 3 b) (1 + a + b)$

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