Question

a+b+c=6 then find (2-a)3+(2-b)3+(2-c)3-3(2-a)(2-b)(2-c)

Answer 1

Hello!
Here is your answer

Given
$a + b + c = 6$
Let

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

$x + y + z = 2 - a + 2 - b + 2 - c$
$x + y + z = 6 - a - b - c$
$x + y + z = 6 - (a + b + c)$
$x + y + z = 6 - 6 = 0$
If
$x + y + z = 0 \\ then \\ x {}^{3} + y {}^{3 } +z {}^{3} = 3xyz$
$xyz =( 2 - a)(2 - b)(2 - c)$
$+ 3xyz - 3xyz = 0$
Answer = 0