Chapter 8.2, Problem 50HP

To determine

To describe: The steps to multiply a polynomial by a monomial.

Answer to Problem 50HP

In order to multiply a monomial and a polynomial, use the distributive property and then use the exponent product property.

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 $2n^2+3n+5$

Write in product form

  $2n\left(2n^2+3n+5\right)$

Now, use distributive property as shown below

  $2n\cdot 2n^2+2n\cdot 3n+2n\cdot 5$

Finally multiply and use the exponent property $x^a\cdot x^b=x^{a+b}$

  $\begin{array}{l}4n^{2+1}+6n^{1+1}+10n\\ =4n^3+6n^2+10n\end{array}$

So, in order to multiply a monomial and a polynomial, use the distributive property and then use the exponent product property.