SOLUTION: Does anyone know how to do this type of problem? I am stuck, and would appreciate any help. Thanks! Factor s^6-729

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Does anyone know how to do this type of problem? I am stuck, and would appreciate any help. Thanks! Factor s^6-729      Log On


   

Question 599123: Does anyone know how to do this type of problem? I am stuck, and would appreciate any help. Thanks!
Factor
s^6-729
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

s%5E6-729 Start with the given expression.


%28s%5E2%29%5E3-%289%29%5E3 Rewrite s%5E6 as %28s%5E2%29%5E3. Rewrite 729 as %289%29%5E3.


%28s%5E2-9%29%28%28s%5E2%29%5E2%2B%28s%5E2%29%289%29%2B%289%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


%28s%5E2-9%29%28s%5E4%2B9s%5E2%2B81%29 Multiply


%28s-3%29%28s%2B3%29%28s%5E4%2B9s%5E2%2B81%29 Now factor s%5E2-9 to get %28s-3%29%28s%2B3%29 (using the difference of squares rule)

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Answer:
So s%5E6-729 factors to %28s-3%29%28s%2B3%29%28s%5E4%2B9s%5E2%2B81%29.

In other words, s%5E6-729=%28s-3%29%28s%2B3%29%28s%5E4%2B9s%5E2%2B81%29 for all values of 's'

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