SOLUTION: Factor the expression: 125a^3-8b^3

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Question 778430: Factor the expression:
125a^3-8b^3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

125a%5E3-8b%5E3 Start with the given expression.


%285a%29%5E3-%282b%29%5E3 Rewrite 125a%5E3 as %285a%29%5E3. Rewrite 8b%5E3 as %282b%29%5E3.


%285a-2b%29%28%285a%29%5E2%2B%285a%29%282b%29%2B%282b%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


%285a-2b%29%2825a%5E2%2B10ab%2B4b%5E2%29 Multiply

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Answer:
So 125a%5E3-8b%5E3 factors to %285a-2b%29%2825a%5E2%2B10ab%2B4b%5E2%29.

In other words, 125a%5E3-8b%5E3=%285a-2b%29%2825a%5E2%2B10ab%2B4b%5E2%29