Q. 240 - Intermediate Algebra

Question

In the following exercises, factor completely.    

$36q^2-100$

Step-by-Step Solution

Answer

The required factors are $(6q-10)(6q+10)$

Step 1. Given Information

The given expression is $36q^2-100$

Step 2. Calculation

We will find the factors by first take the common factor out and then simplify using the property.

$$\begin{gathered} 36q^2-100={\left(6q\right)}^2-{\left(10\right)}^2 \\ =(6q-10)(6q+10) \end{gathered}$$

Step 3. Check

We will verify the factors by multiplying the factors.

$$\begin{gathered} (6q-10)(6q+10)={\left(6q\right)}^2-{\left(10\right)}^2 \\ =36q^2-100 \end{gathered}$$