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Question
(a – 3b)3 + (3b – c)3 + (c – a)3
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Solution
Let (a - 3b) = x, (3b - c) = y, (c - a ) = z
x + y + z = a - 3b + 3b - c + c - a = 0
∵ x + y + z = 0 ∴x3 + y3 + z3 = 3xyz
∴(a - 3b)3 + (3b - c)3 + (c - a)3 = 3(a - 3b)(3b - c)(c - a)
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