Question

factorise:

a.) (a-b)^3+(b-c)^3+(c-a)^3

Answer 1

It is of second degree in a and it is zero at a = b and a = c. The coefficient of a^2 is 3(c-b). Also, the original expression is symmetric w.rt. cyc,ic permutations. You can write the factorized form in the symmetric form

3(a-b)(c-a)(b-c)