Q. 237 - Intermediate Algebra

Question

In the following exercises, factor completely.    

$121r^2-s^2$

Step-by-Step Solution

Answer

The required factors are $(11r+s)(11r-s)$

Step 1. Given Information

The given expression is $121r^2-s^2$

Step 2. Calculation

We will find the factors by using the property.

$$\begin{gathered} 121r^2-s^2={\left(11r\right)}^2-s^2 \\ =(11r+s)(11r-s) \end{gathered}$$

Step 3. Check

We will verify the factors by multiplying the factors.

$$\begin{gathered} (11r+s)(11r-s)={\left(11r\right)}^2-s^2 \\ =121r^2-s^2 \end{gathered}$$