Question

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

Answer 1

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Answer 2

Let a-b=x

Let b-c=y

Let c-a=z

Then x+y+z= a-b+b-c+c-a=0

x^3+y^3+z^3=3xyz

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

=3a-3b+3b-3c+3c-3a

=1