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

(c + d - a - b) (c - d - a + b)

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(c + d - b) (c + d - a - b)

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(c + d + a - b) (c + d - a + b)

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(c + d + a) (c + d + a + b)

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Solution

The correct option is C $(c + d + a - b) (c + d - a + b)$
$2 (a b + c d) - a^{2} - b^{2} + c^{2} + d^{2}$
$= 2 a b + 2 c d - a^{2} - b^{2} + c^{2} + d^{2}$
$= c^{2} + d^{2} + 2 c d - (a^{2} + b^{2} - 2 a b)$
$= (c + d)^{2} - (a - b)^{2}$
$= (c + d + a - b) (c + d - a + b)$

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