# Find the value of this expression

1. Nov 4, 2012

### utkarshakash

1. The problem statement, all variables and given/known data
If $x=2+2^{2/3}+2^{1/3}$, then the value of $x^3-6x^2+6x$ is

2. Relevant equations

3. The attempt at a solution
The very first idea that comes to my mind is to substitute the value of x in the given expression. But that gets very complicated and long as well. Any other ideas?

2. Nov 4, 2012

### Staff: Mentor

I don't think you can avoid this. Simplify as early and as much as possible (e.g. calculate x^2, simplify that and multiply with x to get x^3).

3. Nov 4, 2012

### AJ Bentley

It doesn't look so bad...
x3 is easy since 3s cancel a lot. Then x2 isn't too bad because 2*2 +2*1 = 6 which divides by 3 easily.

It all simplifies nicely as you go along.

4. Nov 4, 2012

### HallsofIvy

Staff Emeritus
You can simplify the calculations a little by writting this as x(6+ x(x- 6)).

5. Nov 4, 2012

### Dick

Try using $x^3-6x^2+6x=(x-2)^3-6x+8$. That actually saves some work.

6. Nov 6, 2012

### utkarshakash

Thanks. It did save a lot of work.