SOLUTION: Can you show me how to factor this ... 27+8t^3

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Question 323030: Can you show me how to factor this ...
27+8t^3
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
It's the sum of 2 cubes. 27 = 3^3, 8t^3 = (2t)^3
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Any sum of cubes,
a%5E3+%2B+b%5E3+=+%28a%2Bb%29%2A%28a%5E2+-+ab+%2B+b%5E2%29

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

27%2B8t%5E3 Start with the given expression.


%283%29%5E3%2B%282t%29%5E3 Rewrite 27 as %283%29%5E3. Rewrite 8t%5E3 as %282t%29%5E3.


%283%2B2t%29%28%283%29%5E2-%283%29%282t%29%2B%282t%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


%283%2B2t%29%289-6t%2B4t%5E2%29 Multiply

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Answer:

So 27%2B8t%5E3 factors to %283%2B2t%29%289-6t%2B4t%5E2%29.

In other words, 27%2B8t%5E3=%283%2B2t%29%289-6t%2B4t%5E2%29