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.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
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.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
8y^{11}+6y^9-2y^7
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.
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