Mathematics
Evaluate and write the answer in factors form :
(3a - 2b)3 + (2b - 5c)3 + (5c - 3a)3
Factorisation
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Answer
We use the identity:
x3 + y3 + z3 = 3xyz, if x + y + z = 0
Let (3a - 2b) = x, (2b - 5c) = y and (5c - 3a) = z.
Then, x + y + z = 3a - 2b + 2b - 5c + 5c - 3a = 0
Since the sum is zero, we apply the identity:
ā (3a - 2b)3 + (2b - 5c)3 + (5c - 2a)3 = 3(3a - 2b)(2b - 5c)(5c - 3a)
Hence, (3a - 2b)3 + (2b - 5c)3 + (5c - 2a)3 = 3(3a - 2b)(2b - 5c)(5c - 3a).
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