SOLUTION: Factor x^3-512

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Question 629844: Factor
x^3-512
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E3-512 Start with the given expression.


%28x%29%5E3-%288%29%5E3 Rewrite x%5E3 as %28x%29%5E3. Rewrite 512 as %288%29%5E3.


%28x-8%29%28%28x%29%5E2%2B%28x%29%288%29%2B%288%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


%28x-8%29%28x%5E2%2B8x%2B64%29 Multiply

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Answer:
So x%5E3-512 factors to %28x-8%29%28x%5E2%2B8x%2B64%29.

In other words, x%5E3-512=%28x-8%29%28x%5E2%2B8x%2B64%29

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