 # Parentheses with Variables

If the parentheses contain variables instead of numbers, you can’t calculate their contents the way you saw it done on the previous page. The reason is that you don’t know what $a+b$ is. Fortunately, there’s a rule you can use:

Rule

### ParenthesesandVariables

 $c×\left(a+b\right)=a×c+b×c$

In other words, each term inside the parentheses is multiplied with the number or variable outside the parentheses. Here’s an example:

Example 1

Expand the parentheses in the expression $2×\left(3-x\right)$

Normally you calculate what’s inside the parentheses first, but as you don’t know what $3-x$ is, you must apply the rule you just saw: $\begin{array}{llll}\hfill 2×\left(3-x\right)& =2×3-2×x\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =6-2x.\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

The parentheses have been expanded, and because you still don’t know what $x$ is, there’s nothing left to do with this expression.

When you’re multiplying two parentheses that contain numbers, you first find out what’s inside each pair of parentheses and multiply those answers with each other.

Example 2

### ParenthesesandNumbers

Compute $\left(3+5\right)×\left(3-2\right)$

This is often written as $\left(3+5\right)\left(3-2\right)$, with the multiplication sign omitted. That doesn’t mean the sign is gone, just that it’s invisible:

 $\left(3+5\right)\left(3-2\right)=8×1=8.$