Question

find the value of (a-b)cube+(b-c)cube +(c-a) cube

Answer 1

Final Answer : 3(a-b) (b-c) (c-a)

Steps:
1) Let x = (a-b)
y= (b-c)
z = (c-a)

2) We know that,
x + y + z = (a - b) + (b-c) + (c-a)
= 0
3) If x + y + z = 0 ,
then x^3 + y^3 + z^3 = 3xyz

Therefore , here
${(a - b)}^{3} + {(b - c)}^{3} + {(c - a)}^{3} = \\ 3(a - b)(b - c)(c - a)$

Answer 2

I given the answer in the form of an image