Adding and Subtracting Linear Expressions - Free Educational videos for Students in K-12

Adding and Subtracting Linear Expressions - By Anywhere Math

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00:0-1	Welcome anywhere . Math . I'm Jeff , Jacobson .
00:01	And today we're gonna talk about adding and subtracting linear
00:05	expressions . Let's get started . Alright before we get
00:26	to the definition of what a linear expression is .
00:30	Here is a table showing examples of three linear expressions
00:35	and here are three non linear expressions . And I
00:39	want to see if you're able to see the difference
00:42	and see if you can figure out what makes a
00:46	linear expression . So I'll give you a second and
00:48	wait . Yeah . Okay . Did you figure it
00:56	out ? Well , hopefully you notice that all the
01:00	exes all the variables in the linear expressions are to
01:04	the first power . There's no X squares and no
01:06	X cubes or any of that . But in the
01:08	non leader expressions , Yeah , we've got an X
01:11	squared uh We've got an X cubed . This is
01:13	just an X . Right , same as up here
01:16	. But we also have an X . Cubed in
01:19	the expression . And here we've got an X .
01:21	To the fifth . It doesn't matter anything about the
01:24	constants . Those don't make a difference , it's all
01:26	about the variables . So the definition for a linear
01:30	expression is an algebraic expression in which the exponents of
01:36	the variable is one . Alright , let's break that
01:38	down a little bit algebraic expression algebraic . That just
01:41	means it has variables . Right expression , there's no
01:45	equal sign , right ? Just like these are all
01:47	expressions , there's no equal sign . Is not an
01:48	equation in which the exponent here here here , up
01:53	here , you can't see it . But there would
01:54	be one . There are the variable is one .
01:56	So that's just like we said that exponents to that
01:59	exponents three , that was five . Those are non
02:03	linear for it to be linear . The exponent on
02:06	the variable has to be one . And the reason
02:08	for that is if you look at the word linear
02:11	, you should notice something in there . Hopefully you
02:14	notice the word line . They're called linear expressions .
02:17	Because if you graph them , you're gonna get a
02:21	straight line no matter which one of these geographic ,
02:24	it's always going to be a straight line . However
02:27	, non linear expressions like an X squared is going
02:30	to look something like this like that and then cube
02:35	. Those look something like this . It's not perfect
02:40	. But uh , those are not straight lines and
02:42	that's why they're called non linear expressions . All right
02:45	, let's get to our first example . Okay .
02:47	Example one . We are finding the sum . We're
02:50	adding linear expressions . So here's a linear expression plus
02:53	another linear expressions . And all we're doing is adding
02:57	them together . Were simplified This big long expression for
03:01	this one . This one's fairly simple . There's nothing
03:03	to distribute . I don't have to use the distributive
03:06	property . Uh and it's addition . So I can
03:09	use a method where we just line them up vertically
03:12	. So I can say X -2 plus three X
03:18	plus eight . So I can think of this as
03:21	this minus two as a negative two because x minus
03:25	two is the same as X plus a negative to
03:28	um And then that's a positive eight . So if
03:30	I add them together , negative two plus eight would
03:33	be six positive six and three X . Sorry three
03:37	X plus X is for X . Again this was
03:41	positive , so that's gonna be plus six . So
03:43	that's the vertical method of adding linear expressions four X
03:48	plus six . Let's look at part B . I'm
03:51	gonna do this a little bit differently , I'm not
03:53	gonna do it vertically like this , I'm just gonna
03:55	add it horizontally . There is nothing to do inside
03:58	the parentheses . I can't simplify these uh linear expressions
04:03	anymore than they already are . There's also nothing to
04:06	distribute . So I can drop the parentheses . So
04:09	I'm gonna rewrite it as just negative four . Y
04:11	plus three plus 11 Y and this minus five .
04:16	I'm going to make it into plus negative five .
04:20	And that just allows me to move things around right
04:23	And I can combine by like terms now . So
04:26	negative four Y plus 11 wise the other like terms
04:31	. So I'll write that there plus three and then
04:34	plus negative five here like terms and here like terms
04:39	, these are the constant when you get really comfortable
04:42	with it . You're gonna be able to do this
04:44	in your head without rearranging . But once you get
04:46	comfortable you probably skip this step negative four Y plus
04:50	11 . Why would give me seven ? Y positive
04:53	three plus a negative five would give me plus -2
05:00	. But we know an expression is not simplified all
05:04	the way until there is no parenthesis . So this
05:08	plus negative two is going to become seven Y -2
05:14	. No more parentheses and no like terms . Let's
05:18	try another example . Okay , example to simplify again
05:22	, first thing I'm always going to look for is
05:24	inside the parenthesis . Is there anything to simplify first
05:28	? There's no like terms here , There's no like
05:30	terms here , so I can't do that . So
05:32	now I'm looking and I see I need to distribute
05:35	this to so that's gonna be my first step .
05:37	The two is gonna be multiplied by all the terms
05:41	inside the parentheses . So two times negative 7.5 x
05:47	would be negative 15 x Plus two times 3 six
05:53	. Uh and then I have plus , since there's
05:56	nothing to do in here , I can get rid
05:58	of those parentheses . Plus five X -2 . Here
06:02	are my terms . I'm going to do something a
06:05	little bit different . I'm not going to rewrite it
06:08	as an addition expression . I'm going to use a
06:12	different method to identify my life terms . I'm gonna
06:14	circle my light terms . Um So this negative 15
06:19	X . Will go blue circle and this uh five
06:23	X . Right there that positive five X . Those
06:26	are like terms . Um I have a positive six
06:28	and a negative too . It's -2 . But we
06:33	know we can rewrite that as plus a negative too
06:37	. When you do this method by circling like terms
06:41	like this whenever you have a subtraction you include that
06:46	with the next term . So it becomes a negative
06:49	whatever . Uh And then all you're doing in between
06:52	the operations in between will always be addition . So
06:56	negative 15 X plus a negative five X . Would
07:01	give me negative 10 X . And then my red
07:06	. These are also like terms , the constant positive
07:09	six plus a negative too would give me positive force
07:14	. So plus four there are no parentheses and there's
07:18	no like terms . So that is simplified as far
07:22	as it can go . Here's some to try on
07:24	your own . Okay here's our last example . We've
07:34	already added linear expressions . Now we're going to subtract
07:38	, we're gonna find the difference of linear expressions .
07:41	Uh So part A five X plus six . That
07:43	linear expression minus negative X plus six for subtraction .
07:48	The way you're going to think about it is this
07:50	subtraction ? We are going to distribute it to all
07:54	the terms inside which means it's just gonna turn everything
07:57	to the opposite . Um if you times everything in
08:01	here by -1 is essentially making them all the opposite
08:04	all the terms . So this is still five X
08:08	plus six . There's nothing to simplify in there so
08:11	I can get rid of the parentheses and then minus
08:14	a negative X . That turns us into plus X
08:19	. And then this minus plus six becomes minus six
08:23	, distribute that to all the terms in here .
08:27	So it changes that negative X . Two positive X
08:30	. And this uh plus six to minus six .
08:33	Now I can just combine my like terms five X
08:37	plus X would give me six X . And plus
08:41	six and a minus six is gonna be zero .
08:44	So that is just going to be six X .
08:47	For part B . Same thing I'm going to need
08:50	to distribute not only this negative or this minus but
08:55	also the two starting here there's nothing to do in
08:58	the parentheses . So again that just is seven Y
09:01	plus five . But then I'm going to distribute a
09:06	negative two . That's really really important when you have
09:11	this minus . And then a number in front of
09:13	parentheses distribute the negative number two the four Y .
09:18	And to the minus three or the negative three negative
09:24	two times four Y . Is gonna be negative eight
09:28	Y negative two times negative three . I'm thinking as
09:33	a negative three because it's minus three is gonna be
09:36	plus six positive six . Now again just combine your
09:41	like terms I have a seven Y . And a
09:46	negative eight Y . And then I also have a
09:51	five . These red square and a six both positive
09:56	. So if I combine those light turns seven Y
10:00	plus a negative eight Y . Is gonna be negative
10:04	one Y . Which I'll just write as negative Y
10:06	plus five plus six is 11 plus 11 . No
10:11	parentheses no like terms . So that is simplified as
10:15	far as it'll go . Here's some more to try
10:18	on your own . As always . Thank you so
10:24	much for watching and if you like this video please
10:26	subscribe . Mhm .

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