Chapter 8.2, Problem 49HP

To determine

To write: A monomial and a polynomial using n as the variable and then find their product.

Answer to Problem 49HP

Monomial: $2n$

Polynomial: $2n^2+3n+5$

Product: $4n^3+6n^2+10n$

Explanation of Solution

Given:

  ${\left(x+2\right)}^2=x^2+2^2$

Calculation:

A monomial with variable n is $2n$

A polynomial with variable n is given by $2n^2+3n+5$

Find their product

  $\begin{array}{l}2n\left(2n^2+3n+5\right)\\ =2n\cdot 2n^2+2n\cdot 3n+2n\cdot 5\\ =4n^3+6n^2+10n\end{array}$