a^7-ab^6=a(a^6-b^6)
=a(a^3+b^3)(a^3-b^3)
=a(a+b)(a^2-ab+b^2)(a-b)(a^2+ab+b^2)
=a(a-b)(a+b)(a^2-ab+b^2)(a^2+ab+b^2)