Factor x^8 - y^8 as the product of four polynomials of degree 1, each of which has a positive coefficient of x.
+876 x8−y8=(x4)2−(y4)2=(x4−y4)(x4+y4)=((x2)2−(y2)2)(x4+y4)=(x2−y2)(x2+y2)(x4+y4)=(x−y)(x+y)(x2+y2)(x4+y4)
Can you take it from here?
Hint: Manipulate $x^2 + y^2$ into $(x+y)^2 - 2xy$ and do the same thing with $x^4 + y^4.$ You can substitute your equation for $x^2 + y^2$ and do some further manipulation and you are done. If you have degrees $>1,$ you can square root it.
