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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 to Chuck
Norris's or maybe it's Chuck nor I and two that I am going to add another three
Chuck Norris's added another 3 Chuck Norris is in this might seem a little
bit obvious but how many Chuck Norris's do I now have well to Chuck Norris's we
can represent this is literally a Chuck Norris plus a Chuck Norris Chuck Norris
plus another Chuck Norris to Chuck Norris is you can also use those two
times Chuck Norris and this is just another way of representing it and 3
Chuck Norris's 3 Chuck Norris's you could do that is 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 12 345
Chuck Norris's so this would be equal to this would be equal to 5 Chuck Norris's
now let's get a little bit more abstract year took Norris is a very tangible
thing so let's go to a little bit more of traditional algebraic notation if I
have 2 X's to access and member to access is what we could do this is to
access or two timed acts and to that I would add 3 X's and to that I would add
three axes how many X's do I have well once again to access this two times
actually could you that is an ex plus an axe we don't know what the value of x is
but whatever that values you can add it to itself and then 3 X's are going to be
that value in green color 3 X'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 one two three four five axes so do X plus three acts is equal to is equal
to five acts and if you think about it all we really did and hope you can
sexually get it is we just added the two numbers that were multiplying the acts
and these numbers the two or the three they're called cora fishman's very fancy
word was just this constant number this regular number that's multiplied by the
variable just added the two of the three to get
your five acts now let's think about this a little bit more let's go back to
this original expression that to Chuck Norris is plus 3 Chuck Norris's let's
say to that we were to add let's say we were to add some type of a let's say we
were to add seven palms over here so this is my drawing of a plum so we have
seven plums post to Chuck Norris's plus 3 Chuck Norris's and let's say that I
had another two plums I add another to plunge year so what would this whole
thing be well I wouldn't have the seven to the to the three plus the two were
adding different things here you have to Chuck Norris isn't 3 Chuck Norris is so
they're still going to simplify 25 Chuck Norris's they would separately think
about the plums we have seven palms are adding another two bombs were going to
have nine plums plus nine Palms so this simplifies 25 2009 plums similarly over
here if I had instead of just two X plus three acts if I had seven why seven why
+ 20 X plus three acts plus two why what do I now have well I can't add the
extras in the wise they could very well represented different number so all I
can do is really add the X's and then I get the five acts and then I'd
separately at the live at seven wise and to that I had two wise I'm gonna have
nine YZ 57 or something and I had to have something I now have nine of that
something so I'm going to have nine wise so you had that in a different color you
add this and this you get that you add the axes you add
the axes you get that right over there so hopefully that makes little sense I
shall try one more idea so given this what would happen if I were to have two
acts plus one plus seven X plus five will once again you might be tempted to
add the 2+2 one but they're adding different things easier to access this
is just the number one so you really just have to add the axis together so
you say well I got two axes and I'm gonna add seven access to that at what that means I now have nine axes
and then separately you'd say well I've got just the abstract number one and
then got another 51 plus five is going to be equal to 6