SOLUTION: how do i factor the expression 256x^6+500x^3y^3 ?

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Question 423885: how do i factor the expression 256x^6+500x^3y^3 ?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
you will need
a^3 (+-) b^3 = (a (+-) b)(a^2(-+) ab + b^2).... (Sum and Difference of Cubes)


256x%5E6+%2B+500x%5E3y%5E3+.....common factor is x%5E3..factor it out
x%5E3%28256x%5E3+%2B+500y%5E3%29+
x%5E3%284%2A64x%5E3+%2B+4%2A125y%5E3%29+
4x%5E3%2864x%5E3+%2B+125y%5E3%29+
4x%5E3%284%5E3%2Ax%5E3+%2B+5%5E3%2Ay%5E3%29+
4x%5E3%28%284x%29%5E3+%2B+%285y%29%5E3%29+.......use the rule a%5E3+%2B+b%5E3%29+=+%28a+%2B+b%29%28a%5E2+-+ab+%2B+b%5E2%29

4x%5E3%28%284x+%2B+5y%29%28%284x%29%5E2-4x%2A5y%2B%285y%29%5E2%29%29+

4x%5E3%28%284x+%2B+5y%29%28%284x%29%5E2-20xy%2B%285y%29%5E2%29%29+

4x%5E3%28%284x+%2B+5y%29%28%284x%29%5E2-20xy%2B%285y%29%5E2%29%29+.......%2816x%5E2-20xy%2B25y%5E2%29+cannot be factored

answer:
4x%5E3%28%284x+%2B+5y%29%28%284x%29%5E2-20xy%2B%285y%29%5E2%29%29+