SOLUTION: Hello. I'm having some difficulty with the following problem. Factor each expression, if possible 8x^6+125y^3 thanks!

Algebra ->  Equations -> SOLUTION: Hello. I'm having some difficulty with the following problem. Factor each expression, if possible 8x^6+125y^3 thanks!      Log On


   

Question 184057: Hello.
I'm having some difficulty with the following problem.
Factor each expression, if possible
8x^6+125y^3
thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

8x%5E6%2B125y%5E3 Start with the given expression.


%282x%5E2%29%5E3%2B%285y%29%5E3 Rewrite 8x%5E6 as %282x%5E2%29%5E3. Rewrite 125y%5E3 as %285y%29%5E3.


%282x%5E2%2B5y%29%28%282x%5E2%29%5E2-%282x%5E2%29%285y%29%2B%285y%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


%282x%5E2%2B5y%29%284x%5E4-10x%5E2y%2B25y%5E2%29 Multiply

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Answer:

So 8x%5E6%2B125y%5E3 factors to %282x%5E2%2B5y%29%284x%5E4-10x%5E2y%2B25y%5E2%29.

In other words, 8x%5E6%2B125y%5E3=%282x%5E2%2B5y%29%284x%5E4-10x%5E2y%2B25y%5E2%29