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### Course: 7th grade (Eureka Math/EngageNY) > Unit 3

Lesson 1: Topic A: Use properties of operations to generate equivalent expressions- Intro to combining like terms
- Combining like terms with negative coefficients & distribution
- Combining like terms with negative coefficients
- Combining like terms with negative coefficients
- Combining like terms with negative coefficients & distribution
- Combining like terms with rational coefficients
- Combining like terms with rational coefficients
- The distributive property with variables
- Factoring with the distributive property
- Distributive property with variables (negative numbers)
- Equivalent expressions: negative numbers & distribution
- Equivalent expressions: negative numbers & distribution
- Interpreting linear expressions: flowers
- Interpreting linear expressions: diamonds
- Interpreting linear expressions

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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?(40 votes)
- Yes we are finding the answer and then simplifying it.(18 votes)

- I get it but im lost on the operations. how do you know when to divide, subtract, add, or multiply?(28 votes)
- 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.(36 votes)

- so am i adding the X's for my answer?(423 votes)
- 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)(176 votes)

- 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 ?(246 votes)- 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.(159 votes)

- Is zero prime, composite or neither?(105 votes)
- Zero is neither. Zero, I've been taught is just zero. Zero is special. So, to answer your question, zero is neither.(66 votes)

- The chuck norris part makes this video better(78 votes)
- Definitely, he is hilarious.(23 votes)

- 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=?(46 votes)- 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.(25 votes)

- this is how u make math interesting(45 votes)
- 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!(17 votes)- 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?(41 votes)

- Is there a way to understand math better?(15 votes)
- the best way to understand math better is by using them regularly and developing understanding of numerical relations.(28 votes)

## Video transcript

Let's say that I've
got 2 Chuck Norrises, or maybe it's Chuck Norri. And to that I am going to
add another 3 Chuck Norrises. So I'm going to add
another 3 Chuck Norrises. And this might seem
a little bit obvious, but how many Chuck
Norrises do I now have? Well, 2 Chuck Norrises,
we can represent this as literally a Chuck
Norris plus a Chuck Norris. So let me do that,
a Chuck Norris plus another Chuck
Norris, 2 Chuck Norrises. You could also do this
2 times Chuck Norris, and this is just another
way of representing it. And 3 Chuck Norrises-- you
could do that as a Chuck Norris plus a Chuck Norris plus
another Chuck Norris. And so we would
have a grand total-- and this might be
very simple for you. But you would have a
grand total of 1, 2, 3, 4, 5 Chuck Norrises. So this would be equal
to 5 Chuck Norrises. Now, let's get a little
bit more abstract here. Chuck Norris is a
very tangible thing. So let's go to a
little bit more of traditional algebraic notation. If I have 2x's and
remember, you could do this as 2x's or 2 times x. And to that, I would add
3x's How many x's do I have? Well, once again,
2x's, that's 2 times x. You could do that
as an x plus an x. We don't know what
the value of x is. But whatever that value is,
we can add it to itself. And then 3x's are they're
going to be that value. Let me do that in
that same green color. 3x's are going to be that
value plus that value plus whatever that value is. And so how many
x's do I now have? Well, I'm going to
have 1, 2, 3, 4, 5 x's. So 2x plus 3x is equal to 5x. And if you think about it, all
we really did-- and hopefully, you conceptually
get it-- is we just added the 2 numbers that
were multiplying the x. And these numbers, the 2 or the
3, they're called coefficients. Very fancy word, but it's
just this constant number, this regular number that's
multiplied by the variable. You just added the 2 and
the 3, to get your 5x. Now, let's think about
this a little bit more. Let's go back to this original
expression, the 2 Chuck Norrises plus 3 Chuck Norrises. Let's say, to that,
we were to add to some type of a-- let's we
were to add 7 plums over here. So this is my drawing of a plum. So we have 7 plums plus 2 Chuck
Norrises plus 3 Chuck Norrises. And let's say that I
add another 2 plums. I add another 2 plums here. So what this whole thing be? Well, I wouldn't add the 7
to the 2 to the 3 plus the 2. We're adding
different things here. You have 2 Chuck Norrises
and 3 Chuck Norrises, so they're still going to
simplify to 5 Chuck Norrises. . And then we would separately
think about the plums. We have 7 plums, and we're
adding another 2 plums. We're going to have 9 plums. Plus 9 plums, so this simplifies
to five Chuck Norrises and 9 plums. Similarly, over here,
instead of just 2x plus 3x, if I had 7y plus 2x plus 3x
plus 2y, what do I now have? Well, I can't add the
x's and the y's. They could very well
represent a different number. So all I can do is
really add the x's. And then I get the 5x. And then, I'd
separately add the y. If I have 7y's and to that I add
2y's, I'm going to have 9y's. If I have 7 of something
and I add 2 of something, I now have 9 of that something. So I'm going to have 9y's. So you add that. Do that in a different color. You add this and this. You get that. You add the x's. You get that right over there. So hopefully, that
makes a little sense. Actually I'll throw
out one more idea. So given this, what would happen
if I were to have 2x plus 1 plus 7x plus 5? Well, once again,
you might be tempted to add the 2 plus
the 1, but they're adding different things. These are 2x's. This is just the number 1. So you really just have
to add the x's together. So you're going to
say, well, I got 2x's. And I'm going to
add 7x's to that. Well, that means
I now have 9x's. And then, separately,
you'd say, well, I've got just the
abstract number 1. And then I've got another 5. 1 plus 5 is going
to be equal to 6.