SOLUTION: Can you help me solve the following problem. It is to Factor the polynomial completely. {{{512y^3-729}}} I really appriciate it. I am not getting this section at all.

Algebra ->  Functions -> SOLUTION: Can you help me solve the following problem. It is to Factor the polynomial completely. {{{512y^3-729}}} I really appriciate it. I am not getting this section at all.      Log On


   

Question 121499: Can you help me solve the following problem. It is to Factor the polynomial completely.
512y%5E3-729
I really appriciate it. I am not getting this section at all.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The trick here is to recognise the given binomial expression as the difference of two cubes.
512y%5E3-729+=+%288y%29%5E3-9%5E3
The difference of two cubes can be factored nicely as follows:
A%5E3-B%5E3+=+%28A-B%29%28A%5E2%2BAB%2BB%5E2%29 so, applying this to your problem:
512y%5E3-729+=+%288y%29%5E3-9%5E3=%288y-9%29%28%288y%29%5E2%2B%288y%29%289%29%2B9%5E2%29 Simplifying this we get:
%288y-9%29%2864y%5E2%2B72y%2B81%29