Combining Like Terms Calculator with Full Solutions

When you are working with a big, complex algebraic expression, it can feel overwhelming trying to simplify and combine like terms with all the different numbers, variables, and exponents.

That’s why I created this free online tool! This combining like terms calculator simplifies any algebraic expression quickly and accurately while providing full detailed solutions that you can trust!

Whether you’re tackling college algebra, intermediate algebra, or just brushing up on math skills, this calculator will save you time and help you understand each step of the process.

Combining Like Terms Calculator

Combine Like Terms Calculator

Enter an algebraic expression:

ex: 3x+2x-5+7, pq+qp, xy^2+yx^2

What Are Like Terms?

Combining like terms is an important skill for simplifying math problems and solving more complex algebra problems later on in your studies.

But first: what are like terms?

In any mathematical expression, like terms are terms that have identical variable parts. What this means is that they have the same variable(s) raised to the same non-negative integer exponent.

For example, 3x and 5x are like terms. While their coefficients are not equal, they have the same variable, x, that has a power of 1 in each term.

By comparison, the terms 3x and 3x² are not considered like terms. Notice that the powers on x in each term are not the same.

You’ll often spot similar terms when working with linear equations, quadratic equations, or any situation where math symbols are used to connect terms. Your task will be to combine like terms in order to simplify the expression you are working with.

How to Combine Like Terms (With Examples)

When combining like terms, we simply add or subtract the coefficients of the terms, while keeping the variable part unchanged.

Here’s a step-by-step explanation you can follow:

Begin by identifying the like terms. Remember, these are terms that have exactly the same variable and exponent.
Group these like terms together.
Next, add or subtract the coefficients of the like terms.
Lastly, rewrite the simplified expression.

Let’s take a look at an example!

Example: Applying the Distributive Property

Simplify the algebraic expression: \(4y + 5y – 3z\).

We begin by identifying the like terms. Notice that 4y and 5y contain the same variable and exponent. Since these terms are added, we can combine them by adding their coefficients and keeping the variable the same.

\[(4 + 5)y – 3z = 9y – 3z\]

Since -3z is not considered a like term, you will notice that it remains in its original position after collecting the two like terms.

Looking for another explanation? Watch this Short!

Why Use a Combining Like Terms Calculator?

Online calculators are helpful tools when you are stuck on your algebra homework or struggling to learn a new concept.

However, math isn’t just about getting the right answer!

That’s why this like terms calculator is more than just a math solver. I developed this tool to be your companion as you work through difficult algebra problems. When you are feeling stuck, use it to help you understand each step of the process!

My students love using online calculators because they:

save so much time when simplifying a long algebraic expression
provide detailed solutions and step-by-step explanations that improve their math skills
are great preparation tools for working with more advanced topics like the quadratic formula or solving complete quadratic equations
are an excellent companion if you feel stuck with your algebra homework

Check out my collection of online math calculators for more helpful tools to master the difficult math concepts you are studying!

To keep practicing, grab some free worksheets from my collection!

With the right practice and the right tools, tackling algebra problems will feel easier and faster than ever!

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