SOLUTION: 125c^6-8d^6 factor completely

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Question 818731: 125c^6-8d^6 factor completely
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
125c%5E6-8d%5E6
The greatest common factor (GCF) is 1 (which we rarely bother factoring out).

Next we try other factoring methods. One of these other methods is to use factoring patterns. And one of these patterns is:
a%5E3-b%5E3+=+%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29
This pattern can be used on our expression because 125c%5E6 is a perfect cube, %285c%5E2%29%5E3, and 8d%5E6 is also a perfect cube, %282d%5E2%29%5E3. Using this pattern we get:

which simplifies to:
%285c%5E2-2d%5E2%29%2825c%5E4%2B10c%5E2+%2A+d%5E2%2B4d%5E4%29
Neither of these factors will factor further, no matter which method we try, so we are finished.