SOLUTION: factor each expression: 4t^5-32T^2

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Question 119396: factor each expression:
4t^5-32T^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4t%5E5-32t%5E2 Start with the given expression


4t%5E2%28t%5E3-8%29 Factor out the GCF 4t%5E2


Now let's focus on the inner expression t%5E3-8


t%5E3-8 Start with the inner expression.


%28t%29%5E3-%282%29%5E3 Rewrite t%5E3 as %28t%29%5E3. Rewrite 8 as %282%29%5E3.


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


%28t-2%29%28t%5E2%2B2t%2B4%29 Multiply


So t%5E3-8 factors to %28t-2%29%28t%5E2%2B2t%2B4%29.



4t%5E2%28t-2%29%28t%5E2%2B2t%2B4%29 Now reintroduce the GCF 4t%5E2




So 4t%5E5-32t%5E2 factors to 4t%5E2%28t-2%29%28t%5E2%2B2t%2B4%29