Chapter 12, Problem 62RE

To determine

To find: The coefficient of $x^3$ in the expansion of ${\left(x-3\right)}^8$ .

Answer to Problem 62RE

The coefficient of $x^3$ is $-13608$ .

Explanation of Solution

The coefficient of $x^3$ is calculated as,

  $\begin{array}{c}Coeffof{x}^7=\left(\begin{array}{l}8\\ 8-3\end{array}\right){\left(-3\right)}^{8-3}{x}^3\\ =\frac{8!}{5!\left(8-5\right)!}{\left(-3\right)}^5{x}^3\\ =-13608x^3\end{array}$

Therefore, the coefficient of $x^3$ is $-13608$ .