Factorise the following:a^2 + b^2 - c^2 - d^2 + 2ab - 2cd - Vidyadip

Question

Factorise the following:$a^2 + b^2 - c^2 - d^2 + 2ab - 2cd$

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Answer

$a^2 + b^2 - c^2 - d^2 + 2ab - 2cd$
$= (a^2 + b^2 + 2ab) - (c^2 + d^2 + 2cd)$
$= (a + b)^2 - (c + d)^2$
$= (a + b + c + d)(a + b - c - d).$

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