SOLUTION: factor 81b^6-3d^6

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Question 265700: factor 81b^6-3d^6
Found 2 solutions by drk, stanbon:
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Here is the original problem.
81b%5E6-3d%5E6
we can rewrite this as
3%5E4b%5E6-3d%5E6
we see a GCF of 3, so taking that out, we get
3%283%5E3b%5E6+-+d%5E6%29
in the parentheses we can rewrite as
3%28%283b%5E2%29%5E3+-+%28d%5E2%29%5E3%29
this is a difference of cubes and we get
3%28%283b%5E2-d%5E2%29%2A%289b%5E4+%2B+3%28bd%29%5E2+%2B+d%5E4%29%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
factor 81b^6-3d^6
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= 3(9b^6 - d^6)
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= 3(3b^3-d^3)(3b^3+d^3)
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Note: The difference and the sum of cubes can be factored
but I am not sure you want the problem to go to that level.
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Cheers,
Stan H.