Binomial Theorem (part 2)

[datahidden]

what should we do for a-b terms

[sameenn]

wow!! thanku so much!!! :)

[Noorabid9]

we use the letter 'i' instead of 'k' whats the difference?

[haurul]

@Noorabid9 there's no difference, you can denote it with whatever you feel for. :)

[curryyuen]

thank you =]

[davidization6]

extrapulate !!!!

[DudeWithAHighKD]

i got a big math test tomorrow and u just saved my ass, thanks dude

[MementoMario]

@youcantbeascoolasme Well hey, at least we can't be as cool as you. ;)

[youcantbeascoolasme]

uuuuuuuuummmmmmmmmmmmm........­. i don't know very much apperantly. X(



[PomboProductions]

Thank you for every doubt you have helped ME clarify! keep it up :P

[ACfireandiceDC]

This is confusing...

[17901000]

i cant believe im actually saying this but, i think...i think i like math o.o

[lucymydog1995]

@17901000 JOIN THE DARK SIDE MAH FREN! WE HAZ MATHZ!

[sweetsforanji]

Why are you so great? You're my saviour! HAHA =))

[andreasggeorgiou000]

Sal you never stop to amaze me!!! AWESOME!!

[gregwithcton]

dude you are plain awesome

[royaltissue]

I honestly wish you were my grade 12 data management teacher. I might not be able to go to college because I am failing this class due to the fact that I am stuck with a very bad teacher. My final exam is tomorrow, I wish i knew of these videos before I wouldve taught myself along with my fellow class mates.

Thanks man you are great

[pureminney22]

well thanks for sharing! 

[ro33han]

Sal, you are a genius nerd who seemingly knows everything and who managed to score a hot wife (yeah, i've noticed) who went to awesome universities and who just got $2 million from google (or some shit) and now just has to spend a few hours a day doodling, who is also loved by every single human who has seen his videos (me included) and must go to bed with an amazing satisfaction. you got it pretty good. also, if i get into med school, i will straight up fly to america and kiss you. (im a guy<3)

[crucio6199]

Thank you for the video! :D



[StaticShock1100]

@Khanacademy What program do you use to do these videos?

[Becmeda]

I AM IN LOVE WITH YOU. Got my college alg test tomorrow and I'm gonna rock that bitch all thanks to you <3

[Helldiv3rr]

The Pascal's triangle was found by the Chinese decades before Pascal was born, he was just lucky that it was named after him :P

[Mr8thsamurai]

he didnt write it, but he says it @13:09

[grapeforeverafter]

this really helped. learned the trick! :) thanks

[mysteryman537]

every new vid i watch of yours is amazing. i always find a new trick what i'd like to call it. and those tricks are kinda like easy as pie :D

[BroadwayBabe8179]

i do home schooling and your the only way i get through it. thank you so much!!

[titerneeg818]

how would you find the coefficients say of a problem such as (x-2y)^19 ?

[ckala13]

@titerneeg818 Maybe you could assign an arbitrary value for "-2y", such as a = -2y for example. Then you could substitute that value back into your original problem, which would then look like (x+a)^19. Then you can use the binomial theorem and calculate it out, substituting "-2y" back in for "a". Once you've determined the coefficients through the method shown in the video, it's just a matter of raising the "-2" to the appropriate power and then taking that number and multiplying it ...

[ckala13]

@titerneeg818 by the appropriate coefficient that you solved for prior, remembering to correct for the appropriate sign change (odd power of "a" will result in a negative sign value, even power of "a" will result in a positive sign value.) Hope that helps.

[titerneeg818]

GOD BLESS YOU

[A1B1O9O9D]

Thank you

Dubai Students

[TrIcKy361]

Awesome thanks for this.

[Mr71seventyone1]

i m ur greatest fan sir and u real king khan

[jreylbc1]

Great help! Thank you!

[downtownal400]

Teaching techniques, explanations, clarity, tricks/shortcuts on all your vids are superb, sir!! Screen visuals? Meh, a little chicken scratchy. Could you write a little bigger and scroll more? Don't forget we can rewind if we need to see something off-screen. Otherwise, you rock!

[toro199999]

thanks Khan

i'm an egyptian mechanical engineer

i really liked you're method of simplifying power 10 polynomial

liked 5/5

[AcutePorphyria]

you, sir, deserve to be the richest motherfucker in the world, who gets to bang any babe he wants, whenever he wants. I was about to fail my further maths course when i found your videos. I understand binomials more that the cleverest guy in our class. I thank you utterly and unequivacobly. (shame you dont teach spelling, eh)

[bajahey]

Amazing! thanks for sharing!

[atatatr]

please could u tell me how it works ive got a test next week, ive studied for ages and literally tried for two hours to work out how plz plz plz tell

great video thanyou

[david0aloha]

I find n choose k to be way more straight forward than the last example, and Pascal's triangle is a nice visual way of doing it. I think it's very cool to see different algorithms for doing it though.

[bilaltariq50]

Sal Khan uses "Wacom Bamboo Tablet" to write. I have seen him writing on CNN

[MrsEnusable]

THANK GOODNESS! I never get this excited about math, but this is awesome!

What about (a - b)^n??????????

[Nick020206]

@MrsEnusable (a - b)^n = (a + (-b))^n, then apply the formula. Just handle the cases where b is an even power correctly.

[lxbo971163]

I don't think it is the easier way to figure out the nCr in your third method. In my mind, though nCr=n!/(r!(n-r)!) seems very complex, but we can smplify ,and get the simpliest expression nCr=n.(n-1)...(n-r+1)/r!. Furthermore ,the procedure in your third method is using the principle in your first method .

[JustForFunTheBand]

Great videos! thank you! Are you writing with a mouse?

[ENM173]

Khan, truly you are a saint.

[ScorchinBeats]

Wow I'm gonna pass my Binomial Theorem test like an hour before everyone else LOL

[theceemabiswas]

You are really something...realyyyyy somerthing

[Sullybahi]

become a youtube partner sal! you upload so many videos and all get thousands of view, just dont stop uploading!

[MelanholicCarnage]

Khan, what program do you use?

[dmahmood00]

THANK YOU!!!

[soniaangel00]

thanks alot for your neat trick at the end of this video..because of you i'm going to save alot of time and be more accurate in my exams..thank u soo muchhh

[Seniorbooboojuice]

thank you for these videos youre an excellent teacher ive gotten more from these lessons than at school.

[shifterdude647]

great explanation!

[piyushthesmart]

Sir who ever has dictated it i have all my due respect from mah heart for u...thankyou for ur class...in youtube

[cloclo900]

your voice is really good and easy to listen to.

[lovefeet201]

learn some CTRL+ Z man, jesus, you always make such a mess with your graphs. disgusting to watch really

[Sch00ls0ut]

Sal, not that it's a big deal, but you forgot the y^10 int the end

[ichinarukurumaki]

he stated that toward the end of presentation

[panamenaporvida]

would the results be different say if the problem was(x-y)^n instead of (x+y)^n??

[Sch00ls0ut]

yes it is different. If it is (x-y)^n, just think of it as

(x+(-y))^n. So for instance, if u are asked to find (x-y)^2

then using the binomial theorem or pascals triangle, substitute in (-y) for y, so u'll get

(x^2)((-y)^0) + 2(x^1)((-y)^1) +(x^0)((-y)^2),

so this is just

x^2 - 2xy + y^2

[mhsamsim]

yea so basically just rotate signs starting positive then negative then positive...

+ - + - + (first positive is for the fist term x^n)

[grime2oo9]

like your vids can you help with factorial

[btkw]

wow now i can win in binomial expansions!

[letzrock05]

sir u forgot the last Y in the example :)

[oldarney]

I was about to make a rule in my brain to not include the last Y^10, thanks. Anyways the first time i raid that comment I read "sir u fagot the last Y in the example"

[TehKGBeast]

I don't think he had room to write it. But if you listen... You'll hear him reference 1y^10 at 13:08.

[dave93vert]

how super fast, when u know that (a+b)^11. if i want the coefficient of the term with x^7, just take out the graphing calc and type 11 nCr 7 and hit enter. by the way nCr is under the math key.

[sweetdoc84]

Ur Awesome

Thanks

[pommes2591]

i have one random question:

do you write with a smart board or actually with your mouse? because I could never write with my mouse like that... :D

[MyOverflow]

My guess is that he's using a tablet computer (i.e. touch screen = mouse click), so he just writes like usual on it.

[aliondeck07]

thank you, you made this subject a little bit clearer to me.

[trillfire]

EZEZEZEZ!

[Manu9324]

Sir u missed the last term in the following example.

i.e) Y to the power 10.

[KAKKAK0]

@Manu9324 i think he ran out of space

[orgminyak]

wow... that last shortcut method owns! i did it like under 2 mins while my friends still struggling (using ur first video method) after 10. Thx very very much.

[Lolzerd]

wow, im learning this in 7th grade :D and i understand it

[damasta00138]

Wow, I feel old...I'm in the 10th grade, and I got it (on my second time around) but I taught myself. It is easy nw, and I just got done proving the Power Rule lim h->0 ((x+h)^n-x^n)/h=nx^n-1

[OnlyChance]

why are yu learning it already!? im on 9th grade D:

[doughboy9mm]

im only in 8th grade and I'm the only one who understands this in my class

[cousinsara]

We're learning this in 9th grade

[Brian626]

WOW LOL. did you figure this out yourself?

[khanacademy]

No. I forget where I learned it but I know that I did learn it from somewhere.

[maxximinus]

The fast method thingy has really helped me and im using it at school, but there are also questions asking to expand stuff like (x+1)^5(2x+1)^4 with two brackets? how wud i use the same method to expand these? :)

[orgminyak]

Haha. i lol'd at brian's comment. Thx alot for putting up the tut. Really appreciate it =]

[WhiteValkery]

@khanacademy

i think they should teach you this at around grade 12

[deathwagon94]

@khanacademy

The correct explanation for you trick is that when we are doing 10x9/2 we are actually doing n(n-1)/2 for n =10 which is equal to nc2 . so we have done this once for the next time we are multiplying with the power of the

term with a power of (n-3) so our the term becomes n(n-1)(n-3)/2 and when we divide it by "r" term we get n(n-1)(n-2)/2x3 which is nc3 and so on for the up coming terms

[asimpleme]

In Canada... you learn this in grade 11 or 12...

[Brian626]

your point? lol

[TakGSeries]

I think asimpleme was just answering eldominicanboy's question, Brian626.

[BryanW3210]

Thats because there is 3 math courses in grade 12 you can take.

1. Data Management- This unit (easy)

2. Advanced Functions

3. Calculus and Vectors

[pnoyguitar]

Lol..you with the X and Y =D

[eldominicanboy]

this is a stupid question: what grade is this normally taught in?

[pnoyguitar]

I believe..College. Because I'm taking this. =D

[thebigdogmassive]

That last method will save me so much time in my exam... thak you, you are a saviour!!!