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

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Solution

Now,
$(a + b) (c - d) + (a - b) (c + d) + 2 (a c + b d)$
$= (a c + b c - a d - b d) + (a c + a d - b c - b d) + 2 (a c + b d)$
$= (a c + a c + 2 a c) + (b c - b c) + (- a d + a d) + (- b d - b d + 2 b d)$
$= 4 a c$ .

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