x8-y8
difference of cubes
(x2-y2)(x4+x2y2+y4)
first polynomial can be factored further
(x+y)(x-y) (x4+x2y2+y4)
next polynomial can be factored further
x4 + 2x2y2-x2y2+y4
x4+2x2y2+y4- x2y2
first three terms factorable by perfect square
(x2+y2)2 - x2y2
(x2+y2)2 - (xy)2
difference of squares again
(x2+y2+xy)(x2+y2-xy)
first polynomials factored form and second polynomials factored form put together
(x+y)(x-y)(x2+y2+xy)(x2+y2-xy)
sorry if formatting is weird