SOLUTION: Please help me understand how to factor this. I understand how to factor quadratic equations but this for some reason throws me for a loop. Thanks in advance. Factor the polynomia

Algebra ->  Functions -> SOLUTION: Please help me understand how to factor this. I understand how to factor quadratic equations but this for some reason throws me for a loop. Thanks in advance. Factor the polynomia      Log On


   

Question 16473: Please help me understand how to factor this. I understand how to factor quadratic equations but this for some reason throws me for a loop. Thanks in advance.
Factor the polynomial 27x^3 - 8y^3.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Ok, let's see if we can unravel the loop that you've ben thrown for.
First, you will need to learn to recognise cubic terms.
27x%5E3+=+%283x%29%5E3 and
8y%5E3+=+%282y%29%5E3 Rewrite your expression:
%283x%29%5E3+-+%282y%29%5E3
Once you see this, then you'll that your polynomial expression is the "difference of two cubes" for which there is a factored form, which, in general, looks like:
A%5E3+-+B%5E3+=+%28A+-+B%29%28A%5E2+%2B+AB+%2B+B%5E2%29 Thus, with no further ado, we can proceed from here.
Simplify.
%283x%29%5E3+-+%282y%29%5E3+=+%283x+-+2y%29%289x%5E2+%2B+6xy+%2B+4y%5E2%29