Chapter 12, Problem 61RE

To determine

To find: The coefficient of $x^7$ in the expansion of ${\left(x+2\right)}^9$ .

Answer to Problem 61RE

The coefficient of $x^7$ is $144$ .

Explanation of Solution

The coefficient of $x^7$ is calculated as,

  $\begin{array}{c}Coeffof{x}^7=\left(\begin{array}{l}9\\ 2\end{array}\right){\left(2\right)}^{9-7}{x}^7\\ =\frac{9!}{2!\left(9-2\right)!}{2}^2{x}^7\\ =144x^7\end{array}$

Therefore, the coefficient of $x^7$ is $144$ .