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Solve the following. (x-y)3​+(y-z)3 + (z-x)3​ = ?
Question

Solve the following.
(x-y)3​+(y-z)3 + (z-x)3​ = ?

A.

3(x-y)(y-z)(z-x)

B.

(x-y) (y-z)(z-x)

C.

(x+y+z) (x² + y² + z²)

D.

3xyz

Correct option is A

Concept Used:
If a + b + c = 0, then a3 + b3 + c3 - 3abc = 0
Solution:
Let (x - y) = a; (y - z) = b; (z - x) = c
a + b + c = x - y + y - z + z - x = 0
(x - y)3 + (y - z)3 + (z - x)3
= 3(x - y)(y - z)(z - x)

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