Q. 223 - Intermediate Algebra

Question

In the following exercises, factor completely. 

$45n^2+60n+20$

Step-by-Step Solution

Answer

The simplified expression is $5{(3n+2)}^2$

Step 1. Given Information

The given expression is $45n^2+60n+20$

Step 2. Calculation

We will find the factor of polynomial by using perfect square trinomial pattern,

$$\begin{gathered} 45n^2+60n+20=5(9n^2+12n+4) \\ =5({\left(3n\right)}^2+2\times 3n\times 3+{\left(2\right)}^2) \\ =5{(3n+2)}^2 \end{gathered}$$