Q. 243 - Intermediate Algebra

Question

In the following exercises, factor completely.   

$m^2+14mn+49n^2$

Step-by-Step Solution

Answer

The required factors are ${(m+7n)}^2$

Step 1. Given Information

The given expression is $m^2+14mn+49n^2$

Step 2. Calculation

We will find the factors by using the perfect square trinomial pattern.

$$\begin{gathered} m^2+14mn+49n^2={\left(m\right)}^2+2\times m\times 7n+{\left(7n\right)}^2 \\ ={(m+7n)}^2 \end{gathered}$$

Step 3. Check

We will verify the factors by multiplying the factors.

$$\begin{gathered} {(m+7n)}^2={\left(m\right)}^2+2\times m\times 7n+{\left(7n\right)}^2 \\ =m^2+14mn+49n^2 \end{gathered}$$