SOLUTION: Divide x^6-y^6 by x^4+x^2y^2 + y^4.

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Question 1133229: Divide x^6-y^6 by x^4+x^2y^2 + y^4.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Think of the dividend as x%5E6%2B0xy%5E5%2B0x%5E2y%5E4%2B0x%5E3y%5E3%2B0x%5E2y%5E4%2B0xy%5E5-y%5E6, and think of the divisor as x%5E4%2B0x%5E3y%2Bx%5E2y%5E2%2B0xy%5E3%2By%5E4.

Answer by ikleyn(52784) About Me  (Show Source):
You can put this solution on YOUR website!
.
  x%5E6+-+y%5E6 = %28x%5E2%29%5E3-%28y%5E2%29%5E3 = 


    Now apply the standard decomposition formula

    a%5E3+-+b%5E3 = %28a-b%29%2A%28a%5E2%2Bab+%2B+b%5E2%29  with  a = x%5E2  and  b = y%5E2. You will get (I am continuing the chain of expressions)



= %28x%5E2+-+y%5E2%29%2A%28x%5E4+%2B+x%5E2%2Ay%5E2+%2B+y%5E4%29.



It means that  x%5E6+-+y%5E6  divided by  x%5E4+%2B+x%5E2%2Ay%5E2+%2B+y%5E4  is  x%5E2+-+y%5E2.    ANSWER

Solved.