SOLUTION: Factor: 125x^3 + 64

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Question 154219: Factor: 125x^3 + 64
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

125x%5E3%2B64 Start with the given expression.


%285x%29%5E3%2B%284%29%5E3 Rewrite 125x%5E3 as %285x%29%5E3. Rewrite 64 as %284%29%5E3.


%285x%2B4%29%28%285x%29%5E2-%285x%29%284%29%2B%284%29%5E2%29 Now factor by using the sum of cubes formula. Remember the sum of cubes formula is A%5E3%2BB%5E3=%28A%2BB%29%28A%5E2-AB%2BB%5E2%29


%285x%2B4%29%2825x%5E2-20x%2B16%29 Multiply

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Answer:

So 125x%5E3%2B64 factors to %285x%2B4%29%2825x%5E2-20x%2B16%29.

In other words, 125x%5E3%2B64=%285x%2B4%29%2825x%5E2-20x%2B16%29