SOLUTION: Factor 27-64a^3

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Question 179583: Factor 27-64a^3
Found 2 solutions by Mathtut, jim_thompson5910:
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
27-64a^3
:
3%5E3-%284a%29%5E3.... use the difference of cubes formula where a is 3 and b is 4a
:
3-4a%29%289%2B12a%2B16a%5E2%29

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

27-64a%5E3 Start with the given expression.


%283%29%5E3-%284a%29%5E3 Rewrite 27 as %283%29%5E3. Rewrite 64a%5E3 as %284a%29%5E3.


%283-4a%29%28%283%29%5E2%2B%283%29%284a%29%2B%284a%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


%283-4a%29%289%2B12a%2B16a%5E2%29 Multiply

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Answer:
So 27-64a%5E3 factors to %283-4a%29%289%2B12a%2B16a%5E2%29.

In other words, 27-64a%5E3=%283-4a%29%289%2B12a%2B16a%5E2%29