SOLUTION: I need help in remeberinng the steps to FACTORING. x^6y^6-x^3y^3

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Question 177257: I need help in remeberinng the steps to FACTORING.
x^6y^6-x^3y^3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E6y%5E6-1x%5E3y%5E3 Start with the given expression


x%5E3y%5E3%28x%5E3y%5E3-1%29 Factor out the GCF x%5E3y%5E3


Now let's focus on the inner expression x%5E3y%5E3-1




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x%5E3y%5E3-1 Start with the inner expression.


%28xy%29%5E3-%281%29%5E3 Rewrite x%5E3y%5E3 as %28xy%29%5E3. Rewrite 1 as %281%29%5E3.


%28xy-1%29%28%28xy%29%5E2%2B%28xy%29%281%29%2B%281%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


%28xy-1%29%28x%5E2y%5E2%2Bxy%2B1%29 Multiply

So x%5E3y%5E3-1 factors to %28xy-1%29%28x%5E2y%5E2%2Bxy%2B1%29.



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Answer:
So x%5E6y%5E6-x%5E3y%5E3 completely factors to x%5E3y%5E3%28xy-1%29%28x%5E2y%5E2%2Bxy%2B1%29