The problem of decomposing of the given expression is well known, as well as its sophisticated solutions. Now, the problem is to find an EASY solution! VERY easy!
Aslanbek Naziev
Note that X^3 + Y^3 = (X+Y)^3 - 3XY(X+Y). Apply this identity, and the answer will follow like magic!
I'm sorry that the problem with such beautiful solution did not attract attention.
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Aslanbek Naziev
Solution.
(a-b)^3 + (b-c)^ + (c-a)^3 = ((a-b)+(b-c))^3 - 3(a-b)(b-c)((a-b)+(b-c)) + (c-a)^3 = (a-c)^3 - 3(a-b)(b-c)(a-c) - (a-c)^3 = 3(a-b)(b-c)(c-a)!
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