x^7+y^7
=x^7-(-y)^7
=[x-(-y)][x^6+x^5*(-y)+x^4*(-y)^2+x^3*(-y)^3+x^2*(-y)^4+x*(-y)^5+(-y)^6]
=(x+y)(x^6-x^5*y+x^4*y^2-x^3*y^3+x^2*y^4-xy^5+y^6)
x^7+y^7
=x^7-(-y)^7
=[x-(-y)][x^6+x^5*(-y)+x^4*(-y)^2+x^3*(-y)^3+x^2*(-y)^4+x*(-y)^5+(-y)^6]
=(x+y)(x^6-x^5*y+x^4*y^2-x^3*y^3+x^2*y^4-xy^5+y^6)