Question

(2-a)^3+(2-b)^3+(2-c)^3 if a+b+c=6

Answer 1

solve like this u will get

Answer 2

Expand all terms using binomial expansion & FOIL then simplify:
Expand[ (2 - a)^3 + (2 - b)^3 + (2 - c)^3 - 3 (2 - a) (2 - b) (2 - c) ]
= 6 a^2 - a^3 - 6 a b + 6 b^2 - b^3 - 6 a c - 6 b c + 3 a b c + 6 c^2 - c^3

2) Factor out -(-6 + a + b + c)
Factor[ 6 a^2 - a^3 - 6 a b + 6 b^2 - b^3 - 6 a c - 6 b c + 3 a b c + 6 c^2 - c^3 ]
= -(-6 + a + b + c) (a^2 - a b + b^2 - a c - b c + c^2)

Since a+b+c=6, -(-6 + a + b + c) = -(-6 + 6) = 0 (left side)
0 * (right side) = 0 * (a^2 - a b + b^2 - a c - b c + c^2) = 0

Answer = 0