Question

factorise (2x-y-z) 3 +(2y-z-x) 3 +(2z-x-y) 3

Answer 1

(2x-y-z)3 +(2y-z-x)3+(2z-x-y)3
6x-3y-3z+6y-3z-3x+6z-3x-3y
6(x+y+z)+6(-y-x-z)

Answer 2

(2x- y- z)+(2y-z-x)+(2z-x-y)
=0
let, a=2x-y-z
b=2y-z-x
c=2z-x-y
since, a+b+c=0
hence, a^3+b^3+c^3=3abc
(2x-y-z)^3+(2y-z-x)^3+(2z-x-y)
=3(2x-y-z)(2y-z-x)(2z-x-y)