SOLUTION: factor completely: 8t^3-27

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Question 316976: factor completely:
8t^3-27
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

8t%5E3-27 Start with the given expression.


%282t%29%5E3-%283%29%5E3 Rewrite 8t%5E3 as %282t%29%5E3. Rewrite 27 as %283%29%5E3.


%282t-3%29%28%282t%29%5E2%2B%282t%29%283%29%2B%283%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


%282t-3%29%284t%5E2%2B6t%2B9%29 Multiply

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Answer:
So 8t%5E3-27 factors to %282t-3%29%284t%5E2%2B6t%2B9%29.

In other words, 8t%5E3-27=%282t-3%29%284t%5E2%2B6t%2B9%29