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

 May 10, 2021
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Simplify the following
\((2y-1)(4y^{10}+2y^9+4y^8+2y^7 + y^6)\)
Express your answer as a polynomial with the degrees of the terms in decreasing order.

 

\(\begin{array}{|rcll|} \hline && \mathbf{(2y-1)(4y^{10}+2y^9+4y^8+2y^7 + y^6)} \\ &=& (2y-1)y^6(4y^4+2y^3+4y^2+2y + 1) \\ &=& y^6(2y-1)(4y^4+2y^3+4y^2+2y + 1) \\ &=& y^6 \left( 2y(4y^4+2y^3+4y^2+2y + 1)-(4y^4+2y^3+4y^2+2y + 1)\right) \\ &=& y^6\left( 8y^5+4y^4+8y^3+4y^2 + 2y -4y^4-2y^3-4y^2-2y - 1 \right) \\ &=& y^6\left( 8y^5+6y^3 - 1 \right) \\ &=& \mathbf{8y^{11}+6y^9-y^6} \\ \hline \end{array}\)

 

laugh

 May 10, 2021

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