Chapter 8.2, Problem 1P

To determine

To find: The simplified form of $5n\left(3n^3-n^2+8\right)$ .

Answer to Problem 1P

The simplified form of $5n\left(3n^3-n^2+8\right)$ is $15n^4+5n^3+40n$ .

Explanation of Solution

Given:

The expression is $5n\left(3n^3-n^2+8\right)$ .

Calculation:

Simplify the expression $5n\left(3n^3-n^2+8\right)$ as follows:

  $\begin{array}{c}5n\left(3n^3-n^2+8\right)=5n\left(3n^3\right)-5n\left(-n^2\right)+5n\left(8\right)\\ =15n^{1+3}+5n^{1+2}+40n\\ =15n^4+5n^3+40n\end{array}$

Thus, the simplified form of $5n\left(3n^3-n^2+8\right)$ is $15n^4+5n^3+40n$ .