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

Algebra - expanding and simplifying brackets - By tecmath

Transcript


00:00	Good day and welcome to the Tech Math channel ,
00:02	we're gonna be having a look at in this video
00:03	, we're going to continue looking at algebra the basics
00:07	of algebra and we're gonna be having a look at
00:09	how to expand uh , factors that are inside brackets
00:14	, inside and outside brackets . So I'll give you
00:16	an example and they'll get a little bit more complex
00:19	as we go along . But say , we had
00:21	say something like this , I have a rectangle and
00:23	I'll write up an algebraic expression , then we'll expand
00:26	it to say we had this particular rectangle here and
00:30	it looked like this . We had a length of
00:33	four and it had a width of X plus two
00:40	. Okay . Yeah . As we have to look
00:43	at in previous videos , we could actually write an
00:44	algebraic expression with this year because the way we do
00:48	this and if you are unsure these check out a
00:50	couple of the earlier videos were made looking at algebra
00:53	with these by the way . Okay . Um now
00:55	, the way that we could write an algebraic expression
00:58	here is as follows . Well , the area ,
01:02	say we wanted to do one for the area here
01:04	. The area is equal to Okay , the length
01:10	times width . Yeah . Area of a rectangle is
01:13	the length times which which is equal to the length
01:15	, which is for here times X plus two .
01:23	And this is where we can actually write this if
01:26	you remember , we don't need to write it as
01:28	four times X . Prize to . We can actually
01:30	just right four expose to like this . So with
01:35	this deal we can actually go through this is actually
01:38	said to be so far in a factory wrist form
01:42	. Okay , we have two factors here , we
01:45	have four and we have X plus two , but
01:47	it's said to be in a factory wrist form ,
01:50	but we can actually expand these particular brackets according to
01:55	this thing called the distributive law , but I'll show
01:58	you how to do this now , as far as
02:00	this goes , we got two particular types of expressions
02:03	uh and the way we do this is we multiply
02:06	basically each term in the brackets here , this X
02:08	here and two here by this first factor here ,
02:12	this four . Okay , so both of these ,
02:15	yeah , XB one applied by the four here And
02:19	in addition to to hear is being multiplied by the
02:21	4th and this is the way we expand the Okay
02:25	, so we start off here four times X is
02:28	four X . And positive too , Times four is
02:35	positive . So we have successfully expanded these brackets out
02:40	. Okay , so what about we are we go
02:45	through and now we actually we take it to the
02:48	next step , we'll do a few of these as
02:49	examples . Okay . They're fairly fairly basic . Okay
02:52	so what about I'll get you to expand a bunch
02:54	of these just to get used to doing these so
03:00	Well that we do see this one here . six
03:05	X . Plus one . So I want you to
03:09	expand this so we're gonna multiply this one by this
03:14	one and we're going to multiply this term by this
03:17	time . Okay . So let's do this six times
03:21	X . We get six X . And six trans
03:26	positive one . We get positive six . Okay .
03:31	We get 6 . 6 plus six . Okay .
03:35	How do you go with that ? Pretty good .
03:37	All right . What about we do a bit more
03:40	of a actually I'll start with a another sort of
03:44	simple example . Then we get into some harder ones
03:46	. So we do this sort of thing where we
03:48	go three X . And then we're going to go
03:54	X . Actually I want to exit I'll do a
03:58	We'll just do a simple one started . We'll do
04:00	three eggs take away for okay okay so we'll do
04:07	this sort of one again . You can sort of
04:09	see we're gonna head there with this . I bet
04:10	now we're going to go three times X . Is
04:14	three X . And three times minus four because the
04:18	whole bit here is minus four is minus 12 and
04:22	it's a bit of a tricky and make sure you
04:23	pay attention to the number here . We have three
04:27	numbers so to speak one of the Caproni . Um
04:29	I know we have three we have X . And
04:31	we also have minus four . Okay these two numbers
04:34	here are positive but we have a minus for you
04:37	so just make sure you pay attention to that when
04:39	you're doing these . Did you go with that one
04:41	Anyway ? We'll go to a harder example now .
04:44	It's not much harder . In fact , it's not
04:46	really that much harder at all . It's just assist
04:50	a different sort of example . So what about if
04:52	we had to say something about these X on the
04:55	outside the brackets here we had X an X plus
05:00	four and we wanted to expand these . So it's
05:04	the same sort of process . That's this number for
05:07	this . Factor times this factor this part by this
05:09	part , extra objects is X squared and X tons
05:16	positive for is positive four . X . Okay .
05:23	Did you get that ? That's not much different really
05:25	, is it ? So another example like this we
05:30	do say something like , okay , I'll go harder
05:33	one here . What about we go minus X .
05:35	O k minus X . And then brackets island X
05:39	take away died . Okay . That's a bit of
05:44	a more difficult one . It's exactly the same process
05:47	. Yeah minus x Times X . Okay , that's
05:50	a bit of a hard one . What do you
05:51	give you get minus X times ? Actually might ,
05:54	even if you get stuck on this occasionally , just
05:56	substitute quickly value in your head . What's like minus
05:58	three times three ? That's like minus nine . But
06:03	so we're gonna end up with a minus X squared
06:07	. Ok . The bonus X squared And then -1
06:13	times -9 . Well the minus times minus is a
06:17	positive so we can end up with a positive answer
06:20	. So x times nine is 9 eggs . Just
06:24	be aware of these if you make a mistake ,
06:26	don't get too despondent with this . Okay . Just
06:28	work out where you make a mistake and try not
06:30	to make that mistake again . Okay . But I
06:32	think everybody makes mistakes when they're doing things , especially
06:35	at the start . Okay . So what about we
06:37	are now go a couple of further sort of ones
06:41	. I'll make a couple of ones that are a
06:44	fair bit harder here . Okay so so I'm gonna
06:46	give you ones that right ? This one five X
06:55	. Plus two . But on top of this one
06:56	I'm gonna do is at the end of this expression
06:58	I'm gonna write minus two X . Okay how would
07:03	you go expanding this and then simplifying it ? Okay
07:08	sorry first off let's expand this . So we're gonna
07:11	go five times X . is five X . Five
07:17	Times positive two is positive 10 . And then we
07:21	had this expression here this -2 x . So this
07:26	is what we've got so far . We can actually
07:28	take this a step further because we have some like
07:30	terms here this five X . And this minus two
07:33	X . So Let's group these together . five x
07:38	-2 x . is three eggs . And we have
07:44	this positive team . Okay so it's a it's a
07:48	bit of an extra step in there . What about
07:51	a couple more of those ? Okay good . That's
07:57	better . So uh rub those out and a couple
08:01	more examples here . I'll get a bit of a
08:03	harder one . What about I do ? What about
08:07	a nice difficult one to d let's get away from
08:11	the excess for the minute we go to D .
08:13	And I'm gonna put a C . Uh take away
08:17	three D . Ah bus five F . -6 .
08:27	Okay . How are you going to go with that
08:31	? It looks pretty difficult . Let's give it a
08:33	guy . First off we're gonna multiply these guys together
08:37	and we're gonna multiply these guys together and we're gonna
08:39	multiply these guys together and we're gonna multiply these guys
08:42	together . So let's do this . Okay so first
08:47	off we have to D . Time see so we're
08:51	gonna end up with and look it's a little thing
08:54	I'd like to do , I like to keep everything
08:55	in alphabetical order . So I'm gonna write these in
08:57	alphabetical order to , okay it's all right my expressions
09:00	we're gonna end up with two C . D .
09:04	Not that it matters if you write to D .
09:06	C . It's equally as correct . Okay so the
09:10	next expression we have we're gonna be having a look
09:13	at please guys three D minus three D . Times
09:19	two D . So minus three tee times two D
09:23	. There are two times 3 is 6 - actually
09:26	two times -3 -6 . Then we're gonna end up
09:30	with time's D . Which is D squared . Okay
09:37	Now I've got two d . times five f .
09:42	Okay so two D . Times five F . First
09:44	let's multiply the coefficients , we have two times five
09:46	is 10 positive 10 and then we have a D
09:52	. And an F . So we just put them
09:53	down times T times F . And then finally we
09:59	have these two expressions , we're multiplying together . These
10:03	two things are multiplied together to D and minus six
10:07	. So first let's multiply these coefficients is too and
10:10	this minus six or two times minus six is minus
10:13	12 . And the problem here , all this goes
10:19	on the end there . So if you have a
10:21	look here , we can't , we actually don't have
10:24	any life terms because CD is different from the square
10:26	is different from D . F . Is different from
10:28	deep , so we actually can't do anything further with
10:31	this . Okay . Um Although we wanted to be
10:36	uh it's actually not that was about to try and
10:39	flavor , but let's let's leave it at that .
10:42	Um I'll give you one last example here . What
10:47	about we do this type of thing ? Uh What
10:50	about I do I times three A plus four and
10:58	I'm going to take this or take away from this
11:03	. Uh two times for a minus seven . Okay
11:14	, This looks pretty difficult now , isn't it ?
11:15	This is this sort of the pinnacle of algebra expressions
11:18	we've had so far , so we've got two sets
11:20	of brackets here and we're gonna , we're going to
11:23	expand them individually and then we're gonna get our answers
11:26	and we're going to put like terms that together and
11:29	simplify it . So let's do this first . So
11:31	first off , we have eight times story like this
11:34	is three A square . Okay , three . We
11:39	have eight times A which is a squared . The
11:41	next one we have is eight times 48 times positive
11:45	for which is positive four plus four . Okay ,
11:53	over here , now , that's that sorted out .
11:55	This brackets really open these brackets over here now .
11:58	Um so we have two Times four . Actually it's
12:04	-2 times four . It'll be careful at eight .
12:06	So -2 times four . We're going to have borders
12:11	. Right ? So we motive for these are Coefficients
12:14	1st -8 A . And then we have -2 .
12:19	So that was those ones , we're gonna have -2
12:22	, 12 minus seven . Which is positive for the
12:26	minus times minus is a positive number . Okay ,
12:29	as you see here , we have couple of expect
12:33	the parts here that are actually like terms a couple
12:37	of terms here , that the same little life terms
12:40	. Okay , so we're gonna first end up was
12:42	going to end up with three A squared . This
12:44	doesn't have any longer terms to it , but here
12:46	we have positive for I tied a tie So for
12:50	a take a is -4 . Okay . And if
12:57	last fall we had this positive 14 . So how
13:00	did you go with those ? Pretty good hopefully .
13:03	Are you getting a really good hang of these right
13:05	now ? Um I'll tell you what let's just go
13:08	one last one . Where what we do is we
13:10	actually make it a a bit of a shape based
13:15	just just wait . Um So what I'm gonna do
13:18	is we'll get a triangle and we'll work out something
13:22	with that . Okay , so first off he's a
13:24	triangle , Nice right angle triangle here that I have
13:30	. We're gonna call this this part here . eight
13:32	and this one here X plus one . So can
13:39	you expand this ? Okay , can you make an
13:42	algebraic expression for the area ? Okay . So the
13:48	area they were triangle . If you're not sure is
13:52	equal to the base , which is this part here
13:58	times are hard divided by two . Okay , so
14:05	let's have a look at this . So what we
14:09	actually have here is we can actually have one of
14:12	these years . We could actually have the base here
14:14	. But let's let's leave this as it's been written
14:17	. Okay , so we have the base which is
14:20	I'd okay , times the height and the height here
14:26	is X plus one . So all up in the
14:28	Bronx , we have X plus one . We put
14:31	this whole thing over . True . Yeah , we
14:39	can take this a step further . Okay , because
14:43	Let's we can expand the brackets . We can also
14:45	divide this eight x 2 . So which everyone do
14:48	you want to do first here ? What about what
14:51	we do ? Is we just we get rid of
14:53	this to here because it's too here two goes into
14:56	this once and two years into this four times .
14:59	And now we can expand our brackets out . We
15:01	have four X . Okay . For those . And
15:05	we also have four times one which is positive for
15:09	. So our area here is equal to four X
15:12	plus four . Okay . It's quite strange when you
15:15	have a look at this over here and realize that
15:17	we can get an expression over here of what the
15:19	actual are The area is . It's kind of cool
15:22	. That's a substitute of Valium and to check that
15:24	. Okay . So what about we call this this
15:26	height here ? We call this exodus seven . Okay
15:31	. Seven Plus one . Is I'd Eight times eight
15:36	, And a half of that is 32 . So
15:38	32 units square . Okay , units squared . And
15:45	does this fit into our formula here ? We call
15:47	this seven . So seven Times four , which is
15:52	28 plus four . It was 32 units squared .
16:00	So expression is looking pretty good there . Okay .
16:03	Hopefully you're finding these . Okay , um next week
16:06	we're going to have a look at us , we're
16:07	gonna look at where we're expanding multiple brackets together .
16:10	Okay . So when we start having a look at
16:13	brackets that look like this here where we can say
16:16	three plus X and maybe x minus four . Okay
16:23	, we're gonna you span these sorts of brackets .
16:25	In fact , we'll probably write them slightly differently .
16:27	But anyway , hopefully I'll see you then they bought

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