Algebra - expanding brackets - binomials - Free Educational videos for Students in K-12

Algebra - expanding brackets - binomials - By tecmath

Transcript


00:0-1	Good day and welcome to the Tech Math channel .
00:02	What we're gonna be having a look at in this
00:03	video is how to expand to factors of this sort
00:08	of type where we have , say something like here
00:11	we go . X bus three and X plus two
00:17	. Okay . And these are said to be ,
00:18	uh , these are expressions with two terms that are
00:21	called binomial . And we're gonna look about how to
00:23	expand these basically multiply these guys together . Yeah .
00:28	Okay . What about I start off straight away with
00:31	this sort of example . Yeah . Say we example
00:36	, this might be say we had a rectangle .
00:39	Okay . And it looked like this and we had
00:43	two sides . We had this site here , which
00:44	was X plus three , And we had this side
00:48	here , which was X-plus two . And if you
00:52	want to work at the area of these , what
00:54	you realize is that the area it's equal to this
00:59	X plus three here . So I'm gonna put this
01:00	in brackets X plus three towards this exports to .
01:06	Okay , so we want to expand these out and
01:09	make it a little bit more simple . So how
01:11	can we go about doing this ? That's not too
01:14	hard . Um Okay , so if we could do
01:18	this , it's pretty much like we were doing in
01:20	the previous video , we're just expanding where we had
01:23	a single set of brackets , but it's just an
01:25	extra bit of a bit of work with it .
01:28	So we're gonna try and create an expression without brackets
01:31	. Now , the way we do this is as
01:33	follows . So first off this term here , we're
01:36	going to look at this first set of brackets over
01:38	here , and we're gonna be multiplying this one by
01:41	this term here , at this time here . Then
01:47	what we're gonna do is going to go to the
01:48	next part of this part of the brackets here .
01:50	There's three part . We're gonna model qualities , what
01:53	this and this one . Yeah . Let me show
01:57	you actually a pretty cool use for this uh in
01:59	a second as well . Okay but we'll just get
02:02	back to this . Okay but first off let's do
02:05	this . So first off I think it's really good
02:08	if you can get this idea and draw these sorts
02:09	of things . So you start off with one and
02:11	you're gonna go to that one there and that one
02:13	there and this one here is going to go to
02:14	this one here and this one here and then you
02:16	can start following the peru . So X . Okay
02:19	first off X . Times X . His X .
02:23	Squared . Okay so that's this particular one we've done
02:27	just here . The next thing we're gonna do is
02:31	this one X . Times two . Okay so X
02:35	times two Is positive two x . Now we're gonna
02:40	go what is three times X , which is three
02:46	years . And then we're gonna have with three Times
02:51	two , which is six . Okay . So we've
02:55	got this answer and we re expanded roll out .
02:58	And you're gonna see that we actually have some like
02:59	terms here , some terms that have the same pro
03:02	you know , all the same letter on them .
03:04	Okay , into the same power . This one is
03:05	different from these ones , but these guys here at
03:08	this time this X squared is said to be different
03:11	because it's the next square , not just applying all
03:13	X . So we're gonna end up with the following
03:15	X squared . Look at this two X and three
03:18	X . We can add these together some two X
03:19	plus three X . It's five X . And this
03:23	here is 62 states is a six . So how
03:27	did you go with that ? Because you got pretty
03:30	good . Now , I'm going to go through a
03:31	couple more examples of these and I want to show
03:33	you something really , really cool about this . Okay
03:36	, well you might find it cool . I find
03:38	it pretty good . Okay , but we'll get to
03:41	that in a second . Okay , so what about
03:45	, I'll give you a couple more examples there ,
03:46	so just get you expanding . Say this one ?
03:50	Yeah , X take four and two X minus one
04:00	. Okay , so it's the same sort of thing
04:01	. You're gonna be multiplying . I'm going to start
04:03	with this exhale and I'm gonna be multiplying first off
04:05	by this one , so X times two X is
04:10	two X squid . This one times this one X
04:16	Times -1 . Its modest X . Okay , now
04:22	I'm going to be looking at this -41 , so
04:24	-4 Times two X -4 . The first I want
04:28	to buy the coefficients -4 times two is more is
04:32	right X . And then last of all we got
04:36	minus four times minus one , so minus times minus
04:40	is a positive , so positive for . And then
04:43	what we can do is we can put life terms
04:44	and you often when you do with this method you're
04:46	gonna find these two middle ones , you can end
04:47	up with two axes . It's quite a common sort
04:50	of thing . Okay , so what we end up
04:52	with these to be the life terms , two X
04:56	squared minus x minus eight X is minus nine X
05:03	. Because that's like minus one here minus one minus
05:06	eight is minus nine cost for . Okay , what
05:11	about I do one ? That's just a little bit
05:13	different from this , but exactly the same in a
05:16	lot of ways . Okay , uh what about I
05:18	do this sort of one here , where I go
05:22	yeah I might just be In the one bracket .
05:28	Yeah and then I'm going to multiply this by why
05:34	? Plus four You go wait a second . What
05:37	happened to all these exes and that sort of deal
05:39	that doesn't really matter treated exactly the same . You're
05:41	just going to end up with a different letter combinations
05:44	. So first off Multiply these two guys eight times
05:47	wide is A . Y . I . Times four
05:52	It's four and that's a positive . Okay minus B
05:58	. Times why is minus the why A minus B
06:04	. Times four is minus fool . Why ? Check
06:09	for any like terms here this is A . B
06:13	. So don't get too caught up with that .
06:14	That looks a bit like a six . I'll put
06:16	a little tail on it there . Um But we
06:18	have no longer terms . Okay so this is our
06:21	answer here . Okay so what about what about I
06:26	just I want to show you something with this .
06:28	First off I'm just gonna go one further example this
06:32	. I'll show you what I wanted to show you
06:34	. Uh Which was this ? I'm gonna go just
06:36	a harder example . So we had to say something
06:37	like seven X . Take away three and I'm going
06:43	to multiply this by two X . Take away or
06:48	plus plus four . Same thing . These two together
06:53	. 1 seven X times two X . Is 14
06:56	X . seven X . Times four is positive 28
07:02	X -3 times two x . It's more than six
07:08	x . And -3 times four is -12 . We
07:13	can Get these two life terms and put them together
07:16	and we're going to end up with 14 x .
07:19	Okay positive 28 X plus six extra positive 28 plus
07:23	Take away six . I apologize . Is positive 22
07:28	X . take away 12 . So how did you
07:32	go with that ? Yeah , hopefully getting those .
07:35	They're fairly basic and they're fairly good once you get
07:38	them . But I just want to show you one
07:39	thing which I find pretty cool with this and this
07:41	is something you may or may not have realized .
07:44	Especially we've seen somewhat earlier videos , which is this
07:48	and it's assisting here . Say I was to give
07:51	you this type of question 13 times 15 I'm going
07:57	to write this somewhat algebraic lee . I'll show you
08:00	what I mean with this . Um this is just
08:02	this is just I find it's pretty cool . Um
08:05	In fact , we can we can even go a
08:07	step further what we call us to exercise like this
08:09	. So I have to call this an X is
08:11	going to equal 10 . We'll give you this little
08:13	x is going to be equal to 10 . So
08:15	our first expression here is X . Plus . That's
08:21	right . And our second expression here is X .
08:26	Plus for Okay , so what are we going to
08:32	get for our answer here ? We're going to get
08:34	and you might even be able to start working on
08:36	a shortcut with this . Okay ? But you'll you'll
08:38	see these . Okay ? So first I'm going to
08:40	end up with X squared , They were gonna end
08:44	up with a three X . And we're going to
08:49	end up with Okay , so x squared and three
08:53	x . Sure . What about it ? I'll slide
08:56	. And I'm I must say I'm doing this ,
08:58	I'm getting a shortcut stage already . I probably shouldn't
09:00	be doing that . So we're gonna go X squared
09:02	. First off , we'll work at five X .
09:04	I apologize . Okay ? So Plus five X .
09:08	But I start to be able to see them straight
09:10	away . Uh Then what we do is we're gonna
09:12	get through here and multiplied by X . We're gonna
09:14	get positive three X . And then we're gonna have
09:19	a look at three times five which is 15 .
09:22	So positive 15 . And if you do this what
09:26	you're gonna get is X . Squared . We're gonna
09:27	put life terms together plus eight X . Plus 15
09:33	. And we can substitute now turn back into our
09:35	values here . Okay ? Uh X . Squared is
09:38	100 plus I . E . D . Plus 15
09:44	which is equal 295 . You work out what 13
09:49	times 15 is and you'll find out that 195 this
09:52	does work okay ? So you can actually use this
09:55	to work out some mathematical things . And there's a
09:58	couple of shortcuts you can take once you start to
10:00	be able to put these together really quickly . You
10:03	can actually start looking at this and saying this is
10:05	going to be um you can actually start looking at
10:07	this and say this is gonna be X squared plus
10:09	eight x plus 15 . So you can start actually
10:12	going well , that's 15 plus 80 there's gonna be
10:15	a 95 plus 101 195 . It's a really quick
10:18	wire doing modification when you start getting used to it
10:21	, especially when you start putting two X . And
10:23	that sort of like for 23 times 15 , just
10:27	something which is kind of interesting I find anyway ,
10:29	so it's a little wider practices as well when you
10:31	first start doing this cut . So in a good
10:36	way of checking your answer , I think when you're
10:37	doing them , so an example , this might be
10:39	saved , we go four x plus one , Uhh
10:46	and we call this one x Plus six . And
10:50	what we do is we are going to say this
10:52	is the same as 41 12 16 because we can
10:58	call extent Yeah , hopefully you go with this idea
11:01	. Okay for we're gonna end up with four X
11:03	. Squared . And as far as the excess go
11:07	, we're going to have this one here four X
11:12	. Times six which is 24 X . We're gonna
11:14	have one X . Okay , take a bit of
11:16	a shortcut here . You're gonna notice you can actually
11:18	do this rainbow multiplication type thing but I'll do it
11:21	the slow way we're gonna get these guys and multiplied
11:23	. You get 24 X . And then a bit
11:26	later on the first one to get is one X
11:28	. 24 X plus one X . Is 25x .
11:32	Okay . It's a little bit of a shortcut .
11:34	You might not want to do them if you're not
11:36	that are confident to start . Okay . And then
11:39	one times six is six . So what answer do
11:43	we have here ? Okay . Let's see . We're
11:46	gonna substitute 10 into X . is equal to 10
11:49	. We're going to get the answer as follows .
11:50	400 plus 250 plus suits . And what does that
11:57	equal to ? 400 , Okay . So how did
12:04	you go with that ? Is that the correct answer
12:06	? You might want to check that out ? Okay
12:08	. Anyway , hopefully that some help to you and
12:11	that's that's how to expand these binomial expressions . So
12:16	we're gonna be having a look at some further algebra
12:18	in a second . We're gonna be using expanding using
12:22	a difference of two squares rule . Okay ? And
12:25	it's not too bad . Okay , we'll see you
12:27	then . Bye .

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