SOLUTION: I need to factor x to the 6th minus y to the 6th two different ways. I know to use the difference of squares and the difference of cubes but I need to see the solution. Thank you

Algebra ->  Exponents -> SOLUTION: I need to factor x to the 6th minus y to the 6th two different ways. I know to use the difference of squares and the difference of cubes but I need to see the solution. Thank you      Log On


   



Question 665017: I need to factor x to the 6th minus y to the 6th two different ways. I know to use the difference of squares and the difference of cubes but I need to see the solution. Thank you in advance.
Answer by kevwill(135) About Me  (Show Source):
You can put this solution on YOUR website!
Using the difference of squares:
x%5E6+-+y%5E6+=+%28x%5E3%29%5E2+-+%28y%5E3%29%5E2
x%5E6+-+y%5E6+=+%28x%5E3+%2B+y%5E3%29+%2A+%28x%5E3+-+y%5E3%29
Each of these terms can be factored using the sum of cubes formula and the difference of cubes formula, so



Using the difference of cubes:
x%5E6+-+y%5E6+=+%28x%5E2%29%5E3+-+%28y%5E2%29%5E3

x%5E6+-+y%5E6+=+%28x%5E2+-+y%5E2%29+%2A+%28x%5E4+%2B+x%5E2y%5E2+%2B+y%5E4%29
The first term can be factored using the difference of squares formula:
x%5E6+-+y%5E6+=+%28x+%2B+y%29+%2A+%28x+-+y%29+%2A+%28x%5E4+%2B+x%5E2y%5E2+%2B+y%5E4%29
And if you deduced that x%5E4+%2B+x%5E2y%5E2+%2B+y%5E4 can be factored into %28x%5E2+%2B+xy+%2B+y%5E2%29+%2A+%28x%5E2+-+xy+%2B+y%5E2%29 you'd be correct, so