<s>[INST] If $x = 3^{1/3} + 3^{2/3} + 3$, find the value of $x^3 - 9x^2 + 18x - 12$ 
If $x = 3^{1/3} + 3^{2/3} + 3$, find the value of $$x^3 - 9x^2 + 18x - 12.$$

This is not a homework problem. I'm not even a student. I'm going through an old textbook. I know this is a simple problem. Can't seem to crack it though.
 [/INST] It makes sense to let $y = x - 3 = 3^{1 \over 3} + 3^{2 \over 3}$. You are to compute
$$(y + 3)^3 -9(y + 3)^2 + 18(y + 3) - 12$$
This works out to 
$$y^3 - 9y - 12$$
Note that $y^3 = (3^{1 \over 3})^3(1 + 3^{1 \over 3})^3 = 3(1 + 3*3^{1 \over 3} + 3*3^{2 \over 3} + 3) = 3(4 + 3y) = 12 + 9y$. Thus $y^3 - 9y - 12 = 0$.
</s>