# How do you use the distributive property with variables?

May 17, 2018

See examples below

#### Explanation:

Whatever is outside of the parenthesis, we must multiply it by all terms on the inside.

Example: $11 \left(3 x + 9 y\right)$

In this case, we would multiply the $11$ by both of the terms in the parenthesis to get

$33 x + 99 y$

What if we have two sets of parenthesis?

$\left(2 x + 8\right) \left(3 x + 11\right)$

We multiply every term in the first parenthesis by everyone in the second. We are essentially doing the distributive property twice.

This method is sometimes called FOIL, standing for Firsts, Outsides, Insides, Lasts. This is the order we multiply in. Going back to our example

$\left(2 x + 8\right) \left(3 x + 11\right)$

• We multiply the first terms: $2 x \cdot 3 x = \textcolor{\lim e}{6 {x}^{2}}$
• Outside terms: $2 x \cdot 11 = \textcolor{\lim e}{22 x}$
• Inside terms: $8 \cdot 3 x = \textcolor{\lim e}{24 x}$
• Last terms: $8 \cdot 11 = \textcolor{\lim e}{88}$

Now we have

$6 {x}^{2} + 22 x + 24 x + 88$ which can be simplified to

$6 {x}^{2} + 46 x + 88$

Hope this helps!