Simplify the following:
(2y + 1)(4y^10 + 2y^9 + 4y^8 + 2y^7 + 2y^6 + 4y^5)
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^6 + 4y^5) =
(2y) ( 4y^10 + 2y^9 + 4y^8 + 2y^7 + 2y^6 + 4y^5) =
8y*11 + 4y^10 + 8y^9 + 4y^8 + 4y^7 + 8y^6 (A)
And
(1) ( 4y^10 + 2y^9 + 4y^8 + 2y^7 + 2y^6 + 4y^5) = 4y^10 + 2y^9 + 4y^8 + 2y^7 + 2y^4 + 4y^5 (B)
So....combining A and B we get
8y^11 + 8y^10 + 10y^9 + 8y^8 + 6y^7 + 10y^6 + 4y^5