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# Intro to combining like terms

Adding like terms is a fundamental concept in algebra. Coefficients are the numbers in front of variables, and they can be added when the variables are the same. For example, 2x + 3x equals 5x. When dealing with different variables, such as x and y, add them separately, resulting in expressions like 5x + 9y. Created by Sal Khan.

## Want to join the conversation?

• So are we basically just simplifying the answer?
• @EDiaz1786

Exactly right! You're pretty much simplifying the answer. A quick tip: If you see two numbers with the same variable and it tells you to add them... Add it! Below is an example of what I mean.

3x + 4x = 7x

In this case, you would only add the whole numbers and not multiply or add the x's, because if you added/multiplied the x's it would come out to be 7x². But later on in Algebra 1, when you get to factoring and multiplying perfect squares that's when you'll multiply the x's AND the numbers. Here's a quick example of what I mean.

7x(2x+4)

This is saying that we distribute the 7x to the 2x and the 4. So the answer will be 14x² + 28x.

Hope this helps!
• I get it but im lost on the operations. how do you know when to divide, subtract, add, or multiply?
• If you are only combining like terms, stick to adding or subtracting. This depends on the coefficients, but we still use the laws of adding and subtracting positive and negative numbers. You would have to add multiply/divide only if you have to distribute something to everything in the parentheses such as 4(3x-4). Once you distribute, you get back to adding/subtracting.
• so am i adding the X's for my answer?
• Yes, and you can also do this with other variables, as long as the variables are the same. (numerical value is just what you add or subtract)
• this might seem kind of strange but when i was trying to figure out how to add like terms i stumbled upon the fact that adding like terms can be solved by doing the distributive property in reverse. i am not sure if this makes sense or not, but it made sense to me.

for example:

2X + 3X = X(2+3)= X(5) = 5X

i do not like learning rules without understanding why the rules work. i know that you are suppose to simply add the coefficients of like terms and be done with the problem. but is that a shortcut/rule that was made instead of doing the distributive property in reverse ?
• That's precisely right. Most people take a more laid-back approach and think that two things plus three things has got to equal five things, but you're right on target that the distributive law is what's going on behind the scenes to make that simple statement work out.
• Is zero prime, composite or neither?
• Zero is neither. Zero, I've been taught is just zero. Zero is special. So, to answer your question, zero is neither.
• The chuck norris part makes this video better
• Definitely, he is hilarious.
• You had to pick Chuck Norris
hahahahahahahahahahahahahahahahahaha
its beautiful!
but still
heres my question,
Could you take the exponents and divide them by itself if one of them is x^2 and it ends up as x=?
• You can't find the value for anything by dividing it by itself. x^2 divided by x^2 equals 1. So, it still is x=?.
And yes, it's hilarious that he chose Chuck Norris as a variable.
• this is how u make math interesting
• I've had to go back on this video over and over, I still don't understand. It may be the fact that I'm just stupid and too slow to catch up with everyone else.
But seriously, here's what I have to say; When you have a simple question, such as this: -n + (-3) + 3n + 5
How do you solve it? Actually, how do you solve most equations? If anyone has an answer, please help!
• When you're combining like terms, you're not actually solving for anything
(It's not an equation if you don't have the equal sign)
Combining like terms just means you add together anything you can.

-n + (-3) +3n +5
In your example, you have two types of numbers. You have numbers that are a multiple of n and you have regular numbers.

The first thing I usually do is rearrange the numbers so that all the like terms or numbers that can be added together, are next to each other, like this:

-n + 3n + (-3) +5

Then you can rearrange it some more to make it clear how to combine the like terms

3n-n + 5-3

2n + 2

Does that help?