Chapter 8.3, Problem 46PPE

To determine

To find:The volume of the prism.

Answer to Problem 46PPE

  $n^3+8n^2+7n+56$

Explanation of Solution

Given information:The dimensions of a rectangular prism are $n,n+7,\text{ and }n+8$ . The formula is $V=lwh$ .

Calculation:The volume of the prism is,

  $\begin{array}{c}V=lwh\\ \begin{array}{l}=n(n+7)(n+8)\\ =(n^2+7)(n+8)[\text{distributing }n\text{]}\\ \text{=}{n}^2(n+8)+7(n+8)[\text{distributing the second factor }(n+8)]\\ =n^3+8n^2+7(n+8)[\text{distributing }{n}^2]\\ =n^3+8n^2+7n+56[\text{distributing 7]}\end{array}\end{array}$ .

Thus, the volume is $n^3+8n^2+7n+56$ .