When adding algebraic expressions, it can seem a bit tough at first. But don't worry! Once you learn the main steps, it gets easier. Let’s go through the process together, step by step.

Step 1: Find Like Terms

The first thing to do is look for like terms in the expressions you want to add.

Like terms are parts that have the same variables and powers.

For example, in the expression $3x + 5x$, both are like terms because they both use the variable $x$.

Step 2: Organize the Expressions

If you have more than one expression, it helps to write them one below the other. Try to line up the like terms.

For instance, if you want to add $2x + 3$ and $4x + 5$, write it like this:

  2x + 3
+ 4x + 5

Step 3: Combine Like Terms

Now that you have your expressions lined up, it’s time to combine the like terms.

This just means you add the numbers in front of those terms, called coefficients.

Let’s keep going with our example:

• The like terms for $x$ are $2x$ and $4x$.
• When you add them, you get $2x + 4x = 6x$.
• The constant terms are $3$ and $5$, which add up like this: $3 + 5 = 8$.

So, when we add $2x + 3$ and $4x + 5$, we get:

$$(2x + 3) + (4x + 5) = 6x + 8$$

Step 4: Write the Final Expression

After you combine all the like terms, write down your final answer. From our example, we found out that:

$$2x + 3 + 4x + 5 = 6x + 8$$

Step 5: Check Your Work

It's always a good idea to double-check your work.

Make sure you found the like terms correctly and that your math is right. You can also plug in a number for $x$ to see if both sides of the equation (the original and the final) match up.

Example Problem

Let’s look at another example: Adding $7y^2 + 5y + 2$ and $3y^2 + 4$.

1. Find like terms:

   • The like terms are $7y^2$ and $3y^2$ (both $y^2$ terms) along with the constants $2$ and $4$.

2. Combine like terms:

   • $7y^2 + 3y^2 = 10y^2$
   • $2 + 4 = 6$

So, the final expression would be:

$$(7y^2 + 5y + 2) + (3y^2 + 4) = 10y^2 + 5y + 6$$

By following these simple steps, you can confidently add algebraic expressions! Keep practicing, and soon you’ll be a pro at this important skill in algebra.