## anonymous 4 years ago Simplify the following

1. anonymous

|dw:1347334599772:dw|

2. anonymous

There isn't much you can do with that. You can try factoring. There's a difference of cubes up top, and the bottom is a square of sorts.

3. anonymous

@CliffSedge I know that the answer should be 2013. I have no idea how to get there though

4. anonymous

Just to make sure we're looking at the same thing, is this what you wrote? $\frac{8-27^n}{4+2 \cdot 3^n +9} \space +2011+3^n$

5. anonymous

yup

6. anonymous

Well if the answer is 2013, then $\frac{8-27^n}{4+2 \cdot 3^n +9} +3^n = 2.$

7. anonymous

Is it possible to add 2^2 to 2?

8. anonymous

The top can be factored as a difference of cubes: $8-27^n = 2^3-3^{3n} = (2-3^n)(4+2 \cdot 3^n+3^{2n})$

9. anonymous

What do you mean, "add 2^2 to 2?" 2^2 = 4, 4+2=6.

10. anonymous

Are you sure that denominator isn't 4+2*3^n+9^n ?

11. anonymous

Then it would work out just fine.

12. anonymous

@CliffSedge Im sure, its just 9.

13. anonymous

$\frac{8-27^n}{4+2 \cdot 3^n +9^n} \space +2011+3^n \rightarrow$ $\frac{2^3-3^{3n}}{4+2 \cdot 3^n +9^n} \space +2011+3^n \rightarrow$ $\frac{(2-3^n)((4+2 \cdot 3^n +9^n)}{4+2 \cdot 3^n +9^n} \space +2011+3^n \rightarrow$ $2-3^n +2011+3^n =2013.$

14. anonymous

Well, that's unfortunate.