Question
Factorise:
(a - b)3 + (b - c)3 + (c - a)3
(a - b)3 + (b - c)3 + (c - a)3
✓
Answer
(a - b)3 + (b - c)3 + (c - a)3
Putting (a - b) = x, (b - c) = y and (c - a) = z
We get: (a - b)3 + (b - c)3 + (c - a)3
= x3 + y3 + z3 [(x + y + z) = (a - b) + (b - c) + (c - a) = 0]
= 3xyz [(x + y + z) = 0 ⇒ x3 + y3 + z3 = 3xyz]
= 3(a - b)(b - c)(c - a)
Putting (a - b) = x, (b - c) = y and (c - a) = z
We get: (a - b)3 + (b - c)3 + (c - a)3
= x3 + y3 + z3 [(x + y + z) = (a - b) + (b - c) + (c - a) = 0]
= 3xyz [(x + y + z) = 0 ⇒ x3 + y3 + z3 = 3xyz]
= 3(a - b)(b - c)(c - a)
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