SOLUTION: please factor out this polynomial. m^6-64n^3 thank you

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Question 187144: please factor out this polynomial.

m^6-64n^3

thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

m%5E6-64n%5E3 Start with the given expression.


%28m%5E2%29%5E3-%284n%29%5E3 Rewrite m%5E6 as %28m%5E2%29%5E3. Rewrite 64n%5E3 as %284n%29%5E3.


%28m%5E2-4n%29%28%28m%5E2%29%5E2%2B%28m%5E2%29%284n%29%2B%284n%29%5E2%29 Now factor by using the difference of cubes formula.


Remember the difference of cubes formula is A%5E3-B%5E3=%28A-B%29%28A%5E2%2BAB%2BB%5E2%29


%28m%5E2-4n%29%28m%5E4%2B4m%5E2n%2B16n%5E2%29 Multiply

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Answer:


So m%5E6-64n%5E3 factors to %28m%5E2-4n%29%28m%5E4%2B4m%5E2n%2B16n%5E2%29.


In other words, m%5E6-64n%5E3=%28m%5E2-4n%29%28m%5E4%2B4m%5E2n%2B16n%5E2%29