Q. 241 - Intermediate Algebra

Question

In the following exercises, factor completely. 

$25w^2-60w+36$

Step-by-Step Solution

Answer

The required factors are ${(5w-6)}^2$

Step 1. Given Information

The given expression is $25w^2-60w+36$

Step 2. Calculation

We will find the factors by using the property.

$$\begin{gathered} 25w^2-60w+36={\left(5w\right)}^2-2\times 5w\times 6+{\left(6\right)}^2 \\ ={(5w-6)}^2 \end{gathered}$$

Step 3. Check

We will verify the factors by multiplying the factors.

$$\begin{gathered} {(5w-6)}^2={\left(5w\right)}^2-2\times 5w\times 6+{\left(6\right)}^2 \\ =25w^2-60w+36 \end{gathered}$$