Mathematics
Evaluate :
(a - b)3 + (b - c)3 + (c - a)3 by writing answer in factors form.
Factorisation
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Answer
We use the identity:
x3 + y3 + z3 = 3xyz, if x + y + z = 0
Let (a - b) = x, (b - c) = y and (c - a) = z.
Then, x + y + z = a - b + b - c + c - a = 0
Since the sum is zero, we apply the identity:
⇒ (a - b)3 + (b - c)3 + (c - a)3 = 3(a - b)(b - c)(c - a)
Hence, (a - b)3 + (b - c)3 + (c - a)3 = 3(a - b)(b - c)(c - a).
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