Main content

### Course: Pre-algebra > Unit 6

Lesson 9: Combining like terms# Combining like terms

In this lesson, we learned how to add and subtract variables, like apples (a) or x's. We discovered that when we combine or take away the same variable, we can simply count them up or down. For example, 5x minus 2x equals 3x. This helps us understand basic algebra concepts. Created by Sal Khan.

## Want to join the conversation?

- i don't under stand at1:20Please help :((12 votes)
- Are you asking about how Sal said that the variable a can represent anything? What Sal meant was that if their is a question like 7b + 4b the variable b would not have to represent a specific object that begins with b. A certain amount of boxes could be the variable n. Also in a problem (lets say 6c + 2c) if the same variable is used that means its the same object. 6c & 2c both represent the same object. Hope this helped!(16 votes)

- We are studying problems that say name the like terms, -x to the 4th the power, 2x to the 3rd power, -5x the 4th power, -8x to the 2nd power, -6x to the 2nd power, -7x the third power and we are given options to choose from. I don't understand what they are asking. Am I supposed to combine like terms?(12 votes)
- Crystal.

When typing exponents, you can use the symbol "^" to mean "raised to the power of" So your equation can be written as

-x^4 + 2x^3 - 5x^4 - 8x^2 - 6x^2 -7x^3

To combine like terms, you want to first reorder the terms so the powers are from highest to lowest.

-x^4 - 5x^4 -7x^3 + 2x^3 - 8x^2 - 6x^2

The like terms can be combined. That is, the terms with the same power can be combined. I'll write it with parenthesis first to show which ones can be combined.

(-1x^4 - 5x^4) + (-7x^3 + 2x^3) + (- 8x^2 - 6x^2)

which when the like terms are combined becomes

- 6x^4 - 5x^3 - 14x^2

I hope that helps answer your question.(10 votes)

*Why do you do it this way?*Basically if you think of 3x + 4x, you add the coefficients to get 7x. The idea behind this strategy is:

3x = x + x + x

4x = x + x + x

Think of x as the number of x-rays printed. Now, count the total number of x-rays: x + x + x + x + x + x + x

That's right! 7x.

Now think of 4f + 4g. f is fruit and g is grain. Grain and fruit are different, and no values are provided so it is not possible to make such conclusions in this expression.(11 votes)- ok so what happens if a question like this occurs : 3a + 9b = ?

Would it be 12ab?(5 votes)- Unless they ask you to do a specific formula like substitution or elimination, that should be right.(9 votes)

- So 100 + 100 + 100c + 100c = 200 + 200c?(9 votes)
- how could I answer something like -6(3+4x) Id really love a response quick since I have a test and I'm barely prepared! D:(8 votes)
- what about when the second number is just a variable like

4a+a=(5 votes)- Well, when any variable is by itself, imagine a one in front of it, because it is 1a. 4a = 4a and 1a = 1*a = a

The answer to 4a+a = 5a

Hope this helped!(5 votes)

- i didn't get points for this! and my teacher gave this "combining like terms to me and my friends what is wrong?(5 votes)
- combing like terms is adding a variables to the same letters(5 votes)

- what would 3a+4A-2a=

is is 5a? or a+4A(4 votes)- if lowercase a and uppercase A was the same variable, then it would indeed be 5a. however, if they are not, then i think it would be a+4A. It truly depends. However, in most times in my 5th grade class, uppercase A usually represents "area", and lowercase a being its own separate variable, so i would naturally say a+4A.(6 votes)

- What about different letters in equations?(2 votes)
- Terms with different letters cannot be combined, for example 3x + 4y.

Have a blessed, wonderful day!(5 votes)

## Video transcript

Let's say that you
started off with 3 apples. And then I were to give you
another 7, another 7 apples. So my question to you-- and
this might be very obvious-- is how many apples
do you now have? And I'll give you a second
to think about that. Well, this is fairly basic. You had 3 apples. Now, I'm going to
give you 7 more. You now have 3 plus 7. You now have 10 apples. But let's say I want to do
the same type of thinking, but I'm too lazy to
write the word "apples." Let's say instead of
writing the word "apples," I just use the letter a. And let's say this is,
say, a different scenario. You start off with 4 apples. And to that, I add
another 2 apples. How many apples do you now have? Instead of writing apples, I'm
just going to write a's here. So how many of these
a's do you now have? And once again, I'll
give you a few seconds to think about that. This also might be a little
bit of common sense for you. If you had 4 of these apples or
whatever these a's represented, if you had 4 of them and
then you add 2 more of them, you're now going to
have 6 of these apples. But once again, we
started off assuming that a's represent apples. But they could have
represented anything. If you have 4 of whatever
a represents, and then you have another 2 of
whatever a represents, you'll now have 6 of
whatever a represents. Or if you just think of it if
I have 4 a's, and then I add another 2 a's, I'm
going to have 6 a's. You can literally think of 4
a's as a plus a plus a plus a. And if to that, I add another
2 a's-- so plus a plus a, that's 2 a's
right over there-- how many a's do I now have? Well, that's 1, 2, 3, 4, 5, 6. I now have 6 a's. So thinking of it that
way, let's get a little bit more abstract. Let's say that I have 5
x's, whatever x represents. x could be some number. So I have 5 of whatever
that number is. And from that, I subtract 2
of whatever that number is. What would this evaluate to? How many of these
x's would I now have? So it's essentially 5x minus
2x is going to be what times x? Once again, I'll give you a
few seconds to think about it. Well, if I have 5 of something
and I subtract 2 of those away, I'm going to have 3 of
that something left. So this is going
to be equal to 3x. 5x minus 2x is equal to 3x. And if you really think
about what that means, five x's are just x plus
x plus x plus x plus x. And then we're going to
take away two of those x's. So take away one x,
take away two x's. You are going to be
left with three x's.