Simplifying algebraic expressions with more than one variable can feel tough at first. But don't worry! Once you understand the steps, it can actually be pretty fun. Let's break it down together.

Step 1: Combine Like Terms

First, look for like terms to combine.

Like terms are the ones that share the same variable.

For example, in the expression $3x + 4y - 2x + y$, we can group the $x$ terms and the $y$ terms together:

• For the $x$ terms: $3x - 2x = 1x$, which we can just write as $x$.

• For the $y$ terms: $4y + y = 5y$.

So our simplified expression now is $x + 5y$.

Step 2: Use the Distributive Property

Next, if you see parentheses in your expression, it’s time to use the distributive property.

For example, with the expression $2(x + 3y) - 4y$, we'll distribute the $2$:

• This means we multiply: $2 \cdot x + 2 \cdot 3y - 4y$ simplifies to $2x + 6y - 4y$.

• Now, combine the $y$ terms: $6y - 4y = 2y$.

So now, the expression is simplified to $2x + 2y$.

Step 3: Write it Neatly

Finally, make sure your expression looks neat.

It's best to write the variables in a standard order, usually alphabetically.

For example, $2x + 2y$ is not only simple but also easy to read!

With practice, you’ll see that simplifying expressions becomes quicker and easier. Just remember to combine like terms, use the distributive property when necessary, and keep your work neat and organized!