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Question
Simplify (a + b + c)2 + (a - b + c)2
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Solution
We have
(a + b + c)2 + (a – b + c)2
= [(a + b + c)2] – [a – b + c]2
= a2 + b2 + c2 + 2ab + 2bc + 2ca – [a2 + b2 + c2 – 2ab – 2bc + 2ca]
= a2 + b2 + c2 + 2ab + 2bc + 2ca – a2 – b2 – c2 + 2ab + 2bc – 2ca
= 4ab + 4bc
∴ (a + b + c)2 – (a – b + c)2 = 4ab + 4bc
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