Question

If a + b + c = 6, find the value of (2 - a) 3 + (2 - b) 3 + (2 - c) 3 -3(2 - a) (2 - a) (2 - b) (2 - c).

Answer 1

if x+y+z=0 then
x^3+y^3+z^3-3xyz==0
here
a+b+c=6---(1)
x=2-a,
y=2-b,
z=2-c

x+y+z=2-a+2-b+2-c

=6-a-b-c
=6-(a+b+c)
=6-6 from(1)
=0
therefore
x^3+y^3+z^3-3xyz=0