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Simplify: $(a - b) (c - d) + (a + b) (c + d)$

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$2 a b + 2 b c$

$a c + b d$

$2 a c - 2 b d$

$2 a c + 2 b d$

answer is D.

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Detailed Solution

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

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

$= a c - a d - b c + b d + a c + a d + b c + b d$

Collecting the like terms together, we get

$= a c + a c - a d + a d - b c + b c + b d + b d$

$= 2 a c + 2 b d$

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