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Question
Simplify.
(a + b) (c − d) + (a − b) (c + d) + 2 (ac + bd)
Solution
(a + b) (c − d) + (a − b) (c + d) + 2 (ac + bd)
= a (c − d) + b (c − d) + a (c + d) − b (c + d) + 2 (ac + bd)
= ac − ad + bc − bd + ac + ad − bc − bd + 2ac + 2bd
= (ac + ac + 2ac) + (ad − ad) + (bc − bc) + (2bd − bd − bd)
= 4ac
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