If x = 2 - 2^1/3 + 2^2/3, then find the value of x3 - 6x2 + 18x.

Answer: Option D

$$\begin{array}{rl}& x=2-2^{\frac{1}{3}}+2^{\frac{2}{3}}\\ & x-2=2^{\frac{2}{3}}-2^{\frac{1}{3}}\\ & {\left(x-2\right)}^3={\left(2^{\frac{2}{3}}-2^{\frac{1}{3}}\right)}^3\\ & x^3-8-3\times 2x\left(x-2\right)=4-2-3\times 2^{\frac{2}{3}}\times 2^{\frac{1}{3}}\left(2^{\frac{2}{3}}-2^{\frac{1}{3}}\right)\\ & x^3-8-6x^2+12x=4-2-6\left(x-2\right)\\ & x^3-8-6x^2+12x=2-6x+12\\ & x^3-6x^2+12x+6x=2+12+8\\ & x^3-6x^2+18x=22\end{array}$$