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

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Solution

$(a + b) (c - d) + (a - b) (c + d)$
$= a (c - d) + b (c - d) + a (c + d) - b (c + d)$
$= a c - a d + b c - b d + a c + a d - b c - b d$
$= 2 a c - 2 b d$
$= 2 (a c - b d)$

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