Solve:
$x^{2} - 2 x y + y^{2} - 2^{2}$

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Solution

given, $x^{2} - 2 x y + y^{2} - 2^{2}$

$= {(x - y)}^{2} - 2^{2} (∵ {(a - b)}^{2} = a^{2} - 2 a b + b^{2})$

$= (x - y - 2) (x - y + 2) (∵ a^{2} - b^{2} = (a - b) (a + b))$

Hence $x^{2} - 2 x y + y^{2} - 2^{2} = (x - y - 2) (x - y + 2)$

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