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Question
Simplify: (a + b)2 – (a – b)2
Solution
Applying the identities
(a + b)2 = a2 + 2ab + b2
(a – b)2 = a2 – 2ab + b2
(a + b)2 – (a – b)2 = a2 + 2ab + b2 – [a2 – 2ab + b2]
= a2 + 2ab + b2 – a2 + 2ab – b2
= a2(1 – 1) + ab(2 + 2) + b2(1 – 1)
= 0a2 + 4ab + 0b2 = 4ab
(a + b)2 – (a – b)2 = 4ab
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