# How do you evaluate (2m - 5n ) ( 2m + 5n )?

Apr 6, 2018

#### Answer:

$4 {m}^{2} - 25 {n}^{2}$

#### Explanation:

The 3 step method to evaluating these expressions is, you first want to distribute $2 m$ in the first parentheses into the second parentheses giving you $4 {m}^{2}$ and $10 m n$.

Next you will want to distribute the $- 5 n$ in the first parentheses into the second parentheses. This gives you $- 10 m n$ and $- 25 {n}^{2}$.

Finally by adding together your like terms $4 {m}^{2} + 10 m n + \left(- 10 m n\right) + \left(- 25 {n}^{2}\right)$ gives us our final answer $4 {m}^{2} - 25 {n}^{2}$.

Hope this helps!

Apr 6, 2018

#### Answer:

$4 {m}^{2} - 25 {n}^{2}$

#### Explanation:

It is important to note that you have a difference of two squares occurring as it is in the format of $\left(a - b\right) \left(a + b\right)$.

Therefore, the answer is ${a}^{2} - {b}^{2}$. By substituting $2 m$ for $a$ and $5 n$ for $b$, you get

${\left(2 m\right)}^{2} - {\left(5 n\right)}^{2}$

This turns out to be

$4 {m}^{2} - 25 {n}^{2}$

since you raise both the variable and its coefficient to the power of two.

You could also just FOIL this out, meaning you multiply the first term by the fourth term, the first term by the third term, the second term by the third term, and the second term by the fourth term. This gets you

${\left(2 m\right)}^{2} - \left(5 n\right) \left(2 m\right) + \left(5 n\right) \left(2 m\right) - {\left(5 n\right)}^{2}$

As you can see, the two $\left(5 n\right) \left(2 m\right)$ terms cancel out since they are equal and have opposite signs. Therefore, you still get

$4 {m}^{2} - 25 {n}^{2}$

Have a good day!