SOLUTION: Please help me factor the following: 81c^6-3f^6

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Question 330985: Please help me factor the following:
81c^6-3f^6
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Factor:
81c%5E6-3f%5E6 First factor a 3.
3%2827c%5E6-f%5E6%29 Notice that the binomial is the difference of two cubes.
3%28%283c%5E2%29%5E3-%28f%5E2%29%5E3%29
The difference of two cubes can be factored thus:
A%5E3-B%5E3+=+%28A-B%29%28A%5E2%2BAB%2BB%5E2%29 and in this problem, A+=+3c%5E2 and B+=+f%5E2 so making the appropriate substitutions, we get:
highlight%283%283c%5E2-f%5E2%29%289c%5E4%2B3c%5E2f%5E2%2Bf%5E4%29%29 and that's the best we can do!