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Homework Statement
Factor x6 - y6
Homework Equations
a3 - b3 = (a - b)(a2 + ab + b2)
a2 - b2 = (a + b)(a - b)
The Attempt at a Solution
I'm confused.
x6 - y6 = (x2)3 - (y2)3 = (x3)2 - (y3)2
So shouldn't they all have the same factors? When I factor (x2)3 - (y2)3 = (x3)2 - (y3)2 I get different results.
(x3)2 - (y3)2
(x3 - y3)(x3 + y3)
(x - y)(x2 + xy + y2)(x + y)(x2 - xy + y2)(x2)3 - (y2)3
(x2 - y2)((x2)2 + x2y2 + (y2)2)
(x – y)(x + y)(x4 + x2y2 + y4)How do you factor (x4 + x2y2 + y4) into (x2 + xy + y2)(x2 - xy + y2)? Online factorers are saying it's not possible.