Question

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

Answer 1

# Question # 10714

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

**Solution.** Using identity $x^{3} + y^{3} + z^{3} - 3xyz = (x + y + z)(x^{2} + y^{2} + z^{2} - xy - yz - xz)$, one can get that $(2 - a)^{3} + (2 - b)^{3} + (2 - c)^{3} - 3(2 - a)(2 - b)(2 - c) = (6 - a - b - c)(\ldots) = 0$.

**Answer** 0.

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