Q. 238 - Intermediate Algebra

Question

In the following exercises, factor completely.  

$49b^2-36a^2$

Step-by-Step Solution

Answer

The required factors are $(7b-6a)(7b+6a)$

Step 1. Given Information

The given expression is $49b^2-36a^2$

Step 2. Calculation

We will find the factors by using the property.

$$\begin{gathered} 49b^2-36a^2={\left(7b\right)}^2-{\left(6a\right)}^2 \\ =(7b-6a)(7b+6a) \end{gathered}$$

Step 3. Check

We will verify the factors by multiplying the factors.

$$\begin{gathered} (7b-6a)(7b+6a)={\left(7b\right)}^2-{\left(6a\right)}^2 \\ =49b^2-36a^2 \end{gathered}$$