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

4 a c

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4 a c - 4 b d

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4 b d

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4 a c + 4 b d

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Solution

The correct option is A $4 a c$
$(a + b) (c - d) + (a - b) (c + d) + 2 (a c + b d)$
$= a (c - d) + b (c - d) + a (c + d) - b (c + d) + 2 (a c + b d)$
$= a c - a d + b c - b d + a c + a d - b c - d b + 2 a c + 2 b d$
$= 4 a c$

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