Chapter 12, Problem 64RE

To determine

To find: The coefficient of $x^6$ in the expansion of ${\left(2x+1\right)}^8$ .

Answer to Problem 64RE

The coefficient of $x^6$ is $1792$ .

Explanation of Solution

The coefficient of $x^6$ is calculated as,

  $\begin{array}{c}Coeffof{x}^6=\left(\begin{array}{l}8\\ 8-6\end{array}\right){\left(1\right)}^{8-6}{\left(2x\right)}^6\\ =\frac{8!}{6!\left(8-6\right)!}{\left(1\right)}^2{\left(2x\right)}^6\\ =1792x^6\end{array}$

Therefore, the coefficient of $x^6$ is $1792$ .