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# Intro to combining like terms

In simple addition we learned to add all the numbers together to get a sum. In algebra, numbers are sometimes attached to variables and we need to make sure that the variables are alike before we add the numbers. Created by Sal Khan.

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.