Question

If x +y+z =6 then the value of (x-1) 3 + (y-2) 3 + (z-3) 3 is a) 3 (x-1)(y +2) (z-3) b) 3(x-1)(y-2)(z-3)

Answer 1

if a+b+c=0 then a3+b3+c3=3abc
here
(x-1) + (y-2) + (z-3)= x+y+z-6=6-6=0 since x+y=z=0

hence
(x-1) 3 + (y-2) 3 + (z-3) 3 is   3(x-1)(y-2)(z-3)