Factorise : $a^{2} - b^{2} - 2 b - 1$

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Solution

$a^{2} - b^{2} - 2 b - 1 = a^{2} - (b^{2} + 2 b + 1) {\begin{matrix} ∵ (a + b)^{2} = a^{2} + b^{2} + 2 a b a^{2} - b^{2} = (a + b) (a - b) \end{matrix}} = (a)^{2} - (b + 1)^{2} = (a + b + 1) (a - b - 1)$

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