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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)
= 2a2 + 0ab + 2b2
= 2a2 + 2b2
= 2(a2 + b2)
∴ (a + b)2 + (a – b)2 = 2(a2 + b2)
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