Question

FACTORIZE :

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

Answer 1

if x+y+z=0,then x^3+y^3+z^3 =3xyz.
compare given problem with above

here
x=a-b
y=b-c
z=c-a

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

therefore
(a-b)^3+(b-c)^3+(c-a)^3 =3(a-b)(b-c)(c-a)

Answer 2

by using the identity 
[a+b+c][a²+b²+c²-ab-bc-ca] = a³+b³+c³-3abc
In that we hav that if [a+b+c] =0 then a³+b³+c³=3abc

so by applying that method
the answer will be 3[a-b][b-c][c-a]

hpe it would be helpful