Simplify: $2 (a b + c d) - a^{2} - b^{2} + c^{2} + d^{2}$

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Solution

Now,
$2 (a b + c d) - a^{2} - b^{2} + c^{2} + d^{2}$
$= (c^{2} + 2 c d + d^{2}) - (a^{2} - 2 a b + b^{2})$
$= (c + d)^{2} - (a - b)^{2}$
$= (c + d + a - b) (c + d - a + b)$

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2 (a b + c d) - a^{2} - b^{2} + c^{2} + d^{2}

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