Question
Simplify: $(a + b)(c - d) + (a - b)(c + d) + 2(ac + bd)$
✓
Answer
$(a + b)(c - d) + (a - b)(c + d) + 2(ac + bd)$
$= a(c - d) + b(c - d) + a(c + d) - b(c + d) + 2ac + 2bd$
$= ac - ad + bc - bd + ac + ad - bc - bd + 2ac + 2bd$
$= ac + ac - ad + ad + bc - bc - bd - bd + 2ac + 2bd$
$= 2ac - 2bd + 2ac + 2bd$
$= 4ac$
$= a(c - d) + b(c - d) + a(c + d) - b(c + d) + 2ac + 2bd$
$= ac - ad + bc - bd + ac + ad - bc - bd + 2ac + 2bd$
$= ac + ac - ad + ad + bc - bc - bd - bd + 2ac + 2bd$
$= 2ac - 2bd + 2ac + 2bd$
$= 4ac$
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