Algebra Tricks - Multiply binomials instantly - Free Educational videos for Students in K-12

Algebra Tricks - Multiply binomials instantly - By tecmath

Transcript


00:00	Good day and welcome to the Tech Math channel .
00:02	What are we having a look at this video is
00:04	how to solve by no meal expressions really , really
00:07	quickly . Okay , and so we're gonna be looking
00:09	at this , We're also gonna be looking at how
00:11	you can check your answers just to make sure you've
00:13	got the right answer in this video , we're going
00:16	to be looking at how to use this to do
00:19	different multiplication techniques that every day , just sort of
00:22	a bit of interest sake stuff . This is going
00:24	to be the first of the video , we're gonna
00:25	be looking at how to do different parts of algebraic
00:28	expressions like this , How to multiply by no meals
00:30	, how to multiply by no meals and try no
00:33	meals , how to multiply . Try no meals ,
00:34	how to multiply pretty much any polynomial type expression .
00:37	We're also going to be having a look a bit
00:39	later on in videos and how to divide with polynomial
00:44	and that sort of deal . Okay , so if
00:45	you're starting this this particular part of algebra , it's
00:48	a really , really great series of videos for you
00:51	. So anyway , the binomial is going to be
00:52	looking at , I'll give you an example of one
00:54	right now where say I'd get you to have a
00:58	look at . Ah multiplying these ones , solving these
01:04	particular by name as if it's a X plus four
01:06	in this bracket and I've got X plus two in
01:10	this bracket here . So how quickly can you solve
01:12	this ? You should be able to do this fairly
01:15	instantly because the answer to this uh is X squared
01:21	plus six X plus . I'd Okay , this is
01:28	something these Bino meals , they're fairly fairly rapid that
01:31	you should be able to solve these and I'll show
01:33	you right now . Hey , I go about getting
01:35	the answer to this pretty much instantly . Okay ,
01:39	so the way I do this is as follows .
01:42	Now , the first thing I do here's what we
01:47	do is we were gonna multiply all expressions here .
01:49	So just just before we start off , I'll explain
01:51	what we're gonna do . We're gonna we're gonna be
01:53	multiplying this X by the X over here , in
01:55	the two over here and then the four by the
01:59	X . Here and the two here . So rather
02:01	doing in the standard way , this is the way
02:03	we're going to be looking at it . So first
02:06	off , we're going to get these two numbers here
02:09	, the ex and the X . We're gonna multiply
02:10	them together . We're gonna get X squared . And
02:12	that's the first part of our answer . We're going
02:15	to leave a space blank here and then we're gonna
02:18	multiply these last parts . Okay , So two times
02:21	4 equals Okay , so we're gonna leave a bit
02:25	of a gap between those . It's a positive eight
02:26	. So I'm gonna put a positive there then .
02:29	What we're gonna do is we're going to do this
02:30	thing called rainbow multiplication . Okay . So we're going
02:33	to be multiplying is these two numbers together and these
02:38	two numbers together ? And by adding these together ,
02:40	we're going to get the middle part of our answer
02:43	. Okay ? So what we have first is X
02:47	times two is two X . We're going to add
02:49	that to four times X which is four X .
02:52	So we're going to get the answer . Put those
02:54	together . We're gonna get six X . Okay two
02:57	X plus four X . Gives us six X .
02:59	So there's our answer . Okay . And you'll probably
03:04	take a slightly different way of doing these when you
03:06	are when you first started doing them . Okay ?
03:09	So you'll probably be looking at these slightly differently .
03:12	But let's just say I'm going to show you how
03:14	you can check your answer fairly quickly with these .
03:16	Okay . Without having to substitute huge values and that
03:19	sort of deal into their the first thing what we
03:21	do is just consider that We're gonna call X one
03:24	. So if we were to do that would make
03:28	this into a one here . So one plus four
03:30	is five , we're gonna multiply this By 1-plus 2
03:36	, which is three . So the answer is 15
03:38	. We can check our answer down here . Okay
03:40	? Because If this is one , this has become
03:44	one of my exes one . So this would be
03:45	one uh six times extra six times one is six
03:49	. And we're gonna add that to eight . So
03:52	these guys here , one by six or seven plus
03:54	eight is 15 . So we checked our answer .
03:58	It's a good answer . Okay , so hopefully you
04:01	like that . Okay , what about I'll give you
04:03	a different one of these , a little bit of
04:06	your show . You also how you can again use
04:08	this for a different type of modification . Just a
04:10	bit of a I'll do this problem first , but
04:13	then we'll have a look at how you can do
04:15	some multiplication and it's just a bit of our interests
04:17	. Take stuff , so I'll give you another one
04:20	of these . What about we do X plus six
04:25	And I'm gonna get you to multiply that by X
04:28	-1 . Okay . You got to go . So
04:33	did you do this ? Did you first off you
04:35	multiply these two numbers together . We get X times
04:38	X . Which is X squared . We're gonna go
04:42	we're gonna leave that space and then we'll go six
04:44	times minus one there . Six times . This is
04:47	a positive six . This is -1-6 times -1 .
04:52	It's minus six . Did you fall for that trick
04:55	? I hope not . Okay then , what we're
04:57	gonna do is this rainbow multiplication . So we're going
04:59	to go six times X . Which is six X
05:03	. And then minus one times X . Which is
05:07	minus one X . 06 and minus one . We
05:12	have 55 Okay . How'd you go with that answer
05:18	? So let's check it to see if it works
05:19	. Okay ? So let's put some values in here
05:22	. So again , we're just going to consider that
05:24	X equals one . A nice easy one to do
05:27	. All right , let's do this . So this
05:30	will make this one plus six or seven and then
05:33	one take one is nothing . So seven take nothing
05:37	zero . And we'll check it out here . So
05:39	this will become one . One plus five take six
05:45	. So one plus five is six . Take six
05:47	equals zero . It all checks out . Our answer
05:51	should be pretty good . All right . I really
05:53	recommend checking your answers to because it's very very easy
05:55	to make mistakes . All right . I'll put another
05:57	one up this time . What I'm gonna do after
05:59	I we sold . But I'm gonna show you how
06:01	you can do some multiplication with this . And that's
06:03	fairly interesting . I think anyway , that's the way
06:06	my brain works . Anyway . So what about we
06:08	make it a bit harder as time ? What about
06:09	we do three x plus two and we're going to
06:14	multiply that boy X plus two . Okay , So
06:20	you try to get the answer here . So ,
06:24	hopefully what you get is you get three X squared
06:28	. Because we're multiplying these guys together , we gonna
06:30	leave a space . We're gonna multiply two and two
06:33	together . We're gonna get four . We're gonna do
06:35	this rainbow modification . So , two x . and
06:39	66 two x . Plus 6 . 6 . He's
06:44	going to be a dick . So plus because it's
06:46	a positive number and that's a positive over here because
06:49	two and two are both positive . So there's an
06:51	answer . Now , we're going to check it again
06:53	really , really quickly just because I think it's really
06:55	good practice to do that . Okay , so this
06:59	becomes three because there's three times , one is three
07:04	, So three plus 2 is five and then one
07:08	plus two , It's three so 3 And five times
07:12	as together we get 15 . And if we just
07:16	substitute one in here , we're gonna end up with
07:17	three plus I'd Plus for . And you see that
07:24	we also get the answer of 15 . So the
07:27	answer is good . Now I said that I was
07:30	going to show you something with this which is I
07:32	find kind of interesting . Okay , Which is this
07:36	? Yeah . So you're gonna see a number here
07:38	that I'll write down . So I actually turned this
07:41	we're substituting this value for 10 here . I'll show
07:44	it to me because we end up with if I
07:45	was to do that and end up with 30 plus
07:47	two . Yeah , you get that . It's a
07:49	32 And I would be times when you vote X
07:52	was 10 that this would be 10 plus two ,
07:56	which is 12 . Okay , so 32 times 12
07:58	a bit of a standard multiplication . Now I'll show
08:00	you what the answer to this will be . Now
08:02	we can work this out . Well , you've already
08:03	worked it out . Pretty much . Look at this
08:06	, this four goes down here latex which is dried
08:12	the it's going here and three X squared two X
08:14	squared is 10 times 10 which is 100 - 384
08:21	. That's your answer . And that actually is .
08:22	That works . It's pretty cool . Right . Okay
08:25	. What about to give you another example of this
08:28	and I'll do that same sort of thing with this
08:30	. Okay . Where we also add in that particular
08:32	next part of it ? Okay . So what about
08:37	we do another example And then I'll give you a
08:40	whole bunch of ones to try on your own .
08:42	So what about we do four x plus six and
08:47	we multiply that by two X plus four . Okay
08:53	. So what are we going to get for this
08:55	? You might pause it and give it a quick
08:57	go or you maybe you've already solved it ? Okay
08:59	. So the answer that you're going to get is
09:00	this we multiply these two together . First to get
09:04	I'll X squared leave that space . We're going to
09:08	go plus six times plus four positive six times positive
09:11	for which is 24 positive 24 . Then what we're
09:17	gonna do is we're gonna do this Rainbow model application
09:19	. So two times 62 x times six is 12
09:23	X plus four times four X . Which is 16
09:26	X . 12 X plus 16 X 28 X .
09:30	It's positive . 28 x . two positive 28 x
09:35	. Okay , check your answer . Okay , so
09:39	4-plus 6 is 10 . We're gonna times that by
09:43	two Plus four which is six . Okay , so
09:48	that Multiplied together , we get 60 And let's have
09:53	a look here . So this is eight plus 28
09:56	plus 24 and there's also add up to 60 .
10:01	Okay , because eight plus 28 36 plus 24 You're
10:05	60 so answer . It's good . Okay . A
10:09	bit of an oversized tick there but it was a
10:12	very good at her . I'll tell you what and
10:14	what I also said , well just expand that out
10:16	. So we did what we did before , where
10:18	are changes to , we'll do it to see what
10:23	we have is 46 times 24 . Okay . We're
10:30	on substituting 10 into the answer And the answer to
10:33	this . You'll see you've got the units party ,
10:35	which is a four . Now there's two here because
10:38	it's a 20 , we're gonna have to carry it
10:39	across over here because this is to this is the
10:41	10th part here . So four we need carry this
10:44	across here . Okay , so two plus 28 is
10:50	30 so I'm gonna put the zero down and carry
10:52	the three over here And 3-plus 8 11 and that's
10:59	our answer . Okay , so you might get this
11:01	idea that you still have to carry things across when
11:03	you do this . It's pretty cool though . Right
11:05	. All right . What about finally I'm going to
11:07	give you a bunch of these to do by yourself
11:11	. Really , really quickly I take I'll answer I'll
11:13	work through the answers with you , but we'll get
11:16	you all get your paws up and give it everything
11:18	you go . So what about we try I'll give
11:19	him here , we've got X plus six X plus
11:26	to give that one to go . Um We give
11:30	What about to put a negative one in there ,
11:32	two x Minour force to be careful that one uh
11:36	X plus site , we'll try another one which is
11:40	going to be three X plus six and four X
11:52	plus two . And then you might see where this
11:54	is going ahead are . You might be able to
11:55	get his hands and really quickly , I'm going to
11:57	do 36 Times 42 , just almost right down to
12:03	42 the wrong way times 42 . Okay . Sorry
12:09	, pause the video , see how you go .
12:11	Okay . Obviously you might notice that these two questions
12:13	are very much related to one another . Okay ,
12:16	so just a little hint there . Okay , so
12:20	how did you go ? Let's check this out .
12:23	Um I wanted to put the answers in green here
12:26	. Uh So we multiply these two first we end
12:28	up with X squared . Then we get to go
12:32	to the last part which is six times two ,
12:35	which is 12 positive . 12 that is and then
12:39	we will do this rainbow multiplication . So two times
12:42	X . And six times X . They're both positive
12:45	. So we're going to end up with the answer
12:46	six plus two which is right eggs occasionally both positive
12:52	. So we can check out our answer there because
12:54	this would become seven and this would be every substituting
12:57	one . This would become one plus 67 1 times
13:02	one plus two is 31 plus six or 71 plus
13:06	two is three . So we multiply them . We
13:07	get 21 and if we add these together one plus
13:10	eight plus 12 , we also get 21 . So
13:12	the answer is checked . All right . Uh What
13:16	about the next one ? We're gonna go X times
13:18	X which is X squared . Now we're going to
13:21	go the glass part which is minus four times eight
13:25	which is minus 32 . Okay . And then we've
13:30	got this part in the middle which is going to
13:32	be with rainbow multiplication eight times x . -4 times
13:36	. Actually eight X . Take away four x .
13:41	Is four X . Okay , take away four is
13:46	four X . Take away four X is for X
13:48	. We can check this one . This will be
13:50	a great one to check . I think you know
13:51	these ones make you feel a bit uncertain . These
13:53	ones with negatives when you first doing them . So
13:56	If we were to substitute in we could put one
13:59	in here would end up with -3 times Because one
14:04	takeaway 4 is -3 -3 times one plus eight which
14:10	was nine . So you're gonna get minus 27 .
14:12	And then we did this we'd go one Plus four
14:15	which is five . Take away 32 is also -27
14:19	. So the answer is correct . Okay what about
14:23	we do this last one ? Okay . Last one
14:26	wrestled related . So they're not they're not yet .
14:28	Okay . You know what I mean ? Anyway So
14:31	three x times four x . Oh wrong pen better
14:35	get rid of that . Three X times four X
14:38	. Is 12 weeks square . Okay we go to
14:44	the last part which is six times 2 which is
14:49	12 It's positive . 12 . Okay then we're going
14:53	to go we're going to go this rainbow multiplication .
14:56	So three X times two which is six X plus
14:59	six times four X . Which is 24 X .
15:03	So 12 plus 24 , 12 24 12 . Sorry
15:10	, my bad , my bad six plus 24 3
15:13	times three X . Times two is six . Last
15:16	24 . His 30 X almost made a little mistake
15:20	there . It happens occasionally . It's been known to
15:23	happen in the past . Okay , so let's check
15:27	our answer idea . I think it might be a
15:28	really really good one to check our answer . Okay
15:30	, so let's go . Three Plus six is 9
15:35	, four Plus two is 6 . We multiply this
15:38	together . 6 , 54 and 12 Plus 30 .
15:44	It's 42 Plus 12 is 54 . And the good
15:47	thing is if I hadn't made that mistake , if
15:49	I had said that was what that was going to
15:51	end up being I think 36 if I hadn't made
15:53	the error was we had to head on with it
15:55	would have shown up there and I would have known
15:56	to pick that up . Okay . So it's a
15:59	really great idea to check your work . Okay ?
16:02	Yeah . You know this last question , you might
16:06	be able to work this out because 36 times 42
16:09	is very similar to this you're going to see here
16:11	. We just substitute of 10 in here in here
16:14	. We'd end up with 36 and this would be
16:15	42 . Okay cause three expo 60 you know all
16:19	this now . So the answer is going to be
16:21	we use this part to make our answer over here
16:23	. The last part is going to be a two
16:25	. Okay . This one is going to get carried
16:27	over here . Okay . So I wanted nothing is
16:31	one . This three is going to get carried over
16:33	here . three plus 2 is five and one .
16:40	So how do you like that ? Hopefully you're going
16:44	to get really , really good with these . In
16:45	the next video , we're going to have a look
16:46	at our multiplying by no meals and try no meals
16:49	together . Okay , So I hope to see you
16:51	then see you next time . Bye .

Summarizer

DESCRIPTION:

OVERVIEW:

Algebra Tricks - Multiply binomials instantly is a free educational video by tecmath.

This page not only allows students and teachers view Algebra Tricks - Multiply binomials instantly videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.