SOLUTION: FACTOR EACH EXPRESSION: 40- 5T CUBED

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Question 119393: FACTOR EACH EXPRESSION:
40- 5T CUBED
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

40-5t%5E3 Start with the given expression


5%288-t%5E3%29 Factor out the GCF 5


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



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


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


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


%282-t%29%284%2B2t%2Bt%5E2%29 Multiply


So 8-t%5E3 factors to %282-t%29%284%2B2t%2Bt%5E2%29.



5%282-t%29%284%2B2t%2Bt%5E2%29 Now reintroduce the GCF




So 40-5t%5E3 factors to 5%282-t%29%284%2B2t%2Bt%5E2%29