SOLUTION: Factor: {{{ 64a^12 - m^3n^12}}}

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Question 603541: Factor: +64a%5E12+-+m%5E3n%5E12
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

64a%5E12-m%5E3n%5E12 Start with the given expression.


%284a%5E4%29%5E3-%28mn%5E4%29%5E3 Rewrite 64a%5E12 as %284a%5E4%29%5E3. Rewrite m%5E3n%5E12 as %28mn%5E4%29%5E3.


%284a%5E4-mn%5E4%29%28%284a%5E4%29%5E2%2B%284a%5E4%29%28mn%5E4%29%2B%28mn%5E4%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


%284a%5E4-mn%5E4%29%2816a%5E8%2B4a%5E4mn%5E4%2Bm%5E2n%5E8%29 Multiply

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Answer:
So 64a%5E12-m%5E3n%5E12 factors to %284a%5E4-mn%5E4%29%2816a%5E8%2B4a%5E4mn%5E4%2Bm%5E2n%5E8%29.

In other words, 64a%5E12-m%5E3n%5E12=%284a%5E4-mn%5E4%29%2816a%5E8%2B4a%5E4mn%5E4%2Bm%5E2n%5E8%29