Simplify the following: $(2y-1)\cdot(4y^{10}+2y^9+4y^8+2y^7).$ Express your answer as a polynomial with the degrees of the terms in decreasing order.
(2y - 1) ( 4y^10 + 2y^9 + 4y^8 + 2y^7) =
2y ( 4y^10 +2y^9 + 4y^8 + 2y^7) - 1 ( 4y^10 + 2y^9 + 4y^8 + 2y^7) =
8y^11 + 4y^10 + 8y^9 + 4y^8 - 4y^10 - 2y^9 - 4y^8 - 2y^7 =
8y^11 + 6y^9 - 2y^7
+501 
