Factorise :- $y^{2} - 1 - 2 x - x^{2}$

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Solution

$y^{2} - 1 - 2 x - x^{2}$
$\Rightarrow y^{2} - (1 + 2 x + x^{2})$
$\Rightarrow y^{2} - (x + 1)^{2}$ $[∵ (x + 1)^{2} = x^{2} + 1 + 2 x]$
$\Rightarrow (y - x - 1) (y + x + 1)$
$[∵ a^{2} - b^{2} = (a + b) (a - b)]$

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