Binomial Theorem (part 2)

[@Peter_1986]

I once solved a binomial in the 6:th power with the distributive property, it was a terrible experience. Thank God for the binomial theorem.

[@the_ramann]

Thank Newton but ok

[@ArnavBarbaad]

He says "I dont know" so often" but in the end he knows everything!! :D

[@Dougan11]

I have learned more math than 18 years of math class watching your videos

[@masterman280]

Your quick method, is so amazing!

[@andreasggeorgiou000]

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

[@Nomad-87]

thanks Khan i'm an egyptian mechanical engineer i really liked you're method of simplifying power 10 polynomial liked 5/5

[@verniellove891]

This was very helpful... High school elective mathematics can be a huge headache this was awesome. Thank you😌😃

[@benjaminprimm8380]

u da real mvp

[@pasmetha]

didn't he forget b^10, near the end of the video?

[@shastrisouky71]

thanks sir. you made it very easy to comprehend your explanation.

[@_nicolecarmela_]

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

[@sebastianblackfyre]

Thats it! I made my mind! Tomorrow Imm going the distance for full time for math quiz

[@HellaPerformance]

SAL!! I KNOW IT'S ALREADY BEEN FOUR YEARS, BUT IT'S NEVER TOO LATE TO LEARN CTRL+Z!!!

[@arifbillahmeskat1724]

Thank you so much Mr. Khan.You have been very helpful

[@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.

[@TheMidgardViking]

Ctrl + Z will help you undo things faster! But I am sure you already know that :) Great Video!

[@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.

[@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!

[@hkhalid1539]

the quickest way to find the binomial coefficient is to use the nCr button found on top of the division button on your calculator. To find the coefficient, you first type the value of n (the power) and then press the nCr button and then input the r (aka k) value.

[@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

[@AthiArivazhagan]

I'm beginning to feel like a MATH god 🎵🎶

[@PomboProductions]

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

[@ChangerTheGame]

"You could call this an Algorithm, or Drawing!" - the logic in this sentence though :P

[@tacoman9696]

This can be used for engineering, but it's mainly used for statistical surveys. Each x and y is how many possible combinations of yeses and nos there can be.

[@aliondeck07]

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

[@chaoszone7560]

so I'm doing higher maths right now but I'm desperate to begin learming advanced higher since my exams are really close and I want to be ahead. And I can confirm that without these videos, I wouldn't be learning anything

[@c3301-s3y]

u r a super duper awesome guys. thank u sir for the help

[@laladsouza6027]

You saved me dude had it for engineering forgot d basics Ty very much

[@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

[@Creativetechz2093]

i m ur greatest fan sir and u real king khan

[@bajahey]

Amazing! thanks for sharing!

[@shifterdude]

great explanation!

[@chasolsen5034]

Great method! Ty

[@StaticShock1100]

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

[@grapeforeverafter]

this really helped. learned the trick! :) thanks

[@drevialzerathustra5336]

so, is this a good substitute for factorials with binomial expansion?

[@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.

[@jreylbc1]

Great help! Thank you!

[@full109]

why dont my school have math instructors like you!!!!!???? >:[ Man the education of today

[@RomanNumural9]

This video should be titled: how to cheat on you math test in high school XD. Where i live, this is literally the last lesson of the last math class of high school. It is like i have transcended to become a math god :D

[@eruditeswagTV]

Why does the really quick method work? Also why do opposite charges attract?

[@jcbrpt860freakincook]

How can I solve (a+b)^7 as 7 being an odd no. it has no middle term and how would it work with coefficients by which Sal taught, the faster way?

[@stanleykamwende5514]

you forgot y^10 term

[@kulanimukansi6634]

So how did you get the exponents?

[@Monkey_slapping_keys]

Awesome thanks for this.

[@saqibdhuka7150]

I have a question that what it the x and y both already have a coefficient in the question for example like : (3x^2 + 6Y^5)^4.... how would you do that using this method shown in the video..... btw nice tutorial thanks a lot. !!! :-D

[@Reydriel]

Try using substitution (set those terms to something easy like a and b), work it out, then sub them original values back in, then simplify :)

[@saqibdhuka7150]

Thanks a lot :-D

[@TheGamecheater100]

can you split radicals with this theorem?

[@IraCruzLoveR31]

can i still use the pascal's triangle even if the coeffecient is not 1 ex. (2a+4b)^5

[@deepakgotpagar8927]

what we do if there is coefficient of x and y already in bracket

[@datahidden]

what should we do for a-b terms

[@sweetsforanji]

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

[@fabse64]

Mind has been blown.

[@burhanuddinabbas2006]

sir you forgot to add y^10 ,plzz just add the annotation at 9:38

[@MohammadZulfikar]

What if the questio is (a-b)^3 or (a-b)^4 instead of (a+b)^3 & (a+b)^4 ?

[@rickandelon9374]

Same only sign different on the first symmetry!

[@7neoxis1337]

Its an Australian School system thing. Half Yearlies mean the major test half way through the year.

[@khanacademy]

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

[@mirroronoa2280]

or just use nCr , where C is already given in the calculator.. so sal's method is quite tedious and you wont really have all day to to one math , and chances are you are going to make mistakes doing this method..

[@amrsameh1087]

wow, they give you binomial theorem questions on papers where calculators are allowed? That's cute.

[@brazil004]

what do you do when x or y is a value like 2 3 or 4? or y is negative? and exponent is 5 or worse 10?!

[@orgminyak]

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

[@kasai1701]

Super cool

[@eldominicanboy]

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

[@AmineChM21]

dj snake ,lil jon -Bring down the one

[@Becmeda]

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

[@jaeti1643]

What was that now? "i got this for my yr 11 half yearly tomorow"... What is a yr 11 half yearly?

[@janfrompolde]

@Noorabid9 There is no difference. One can use any letter just like with any other variables. Whether one uses k, i, y, x or p or anything else is a matter of personal preference.

[@sweetdoc84]

Ur Awesome Thanks

[@Brian626]

WOW LOL. did you figure this out yourself?

[@dkrIlI]

do u teach chemistry?

[@vatnidd]

Yes, check the playlist called "Chemistry" and "Organic Chemistry".

[@prateekgurjar1651]

+nilesh krishnakumar Go to khanacademy.org

[@dmahmood00]

THANK YOU!!!

[@khlaqila]

I find it sad that I'm going to have this for my gr 9 finals tomorrow.

[@sebastianblackfyre]

Going the distance

[@A1B1O9O9D]

Thank you Dubai Students

[@Peter_1986]

Äh det var inte så farligt, jag hade ingenting speciellt för mig i alla fall. xD

[@btkw]

wow now i can win in binomial expansions!

[@mhsamsim]

yea so basically just rotate signs starting positive then negative then positive... + - + - + (first positive is for the fist term x^n)

[@letzrock05]

sir u forgot the last Y in the example :)

[@Peter_1986]

KhanAcademy >>> most math books.

[@WhiteValkery]

@khanacademy i think they should teach you this at around grade 12

[@cousinsara]

We're learning this in 9th grade

[@curryyuen]

thank you =]

[@TheIdeanator]

undo = ctrl+z also, mind = blown for all values of mind that belong to me.

[@Mr8thsamurai]

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

[@tharunishadi3980]

thanks

[@georgesyropoulos5856]

Sam Winchester is that you ?

[@ShivaShakti-p2e]

I did (a+b)²⁰ it's correct till 6th term 15504 x¹⁵ y ⁵ by the last method and the 7th term getting the wrong coefficient 58140 by that method but by computing for 7th term= ?? coefficient of the 6th term, 15504•x¹⁵/6th , (15504•15)/6 will get 58140 x¹⁴ y⁶ the 7th term but that's wrong

[@m.moanis]

pascal triangle (y)

[@trillfire]

EZEZEZEZ!

[@doughboy9mm]

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

[@sebastianblackfyre]

Wow. Can’t believe the comment is 13 years ago

[@sebastianblackfyre]

Your 26 now

[@7neoxis1337]

Lol i got this for my yr 11 half yearly tomorow :< .....

[@davidization6]

extrapulate !!!!

[@JaredVu213]

you are missing y^10

[@Brian626]

your point? lol

[@ALDIRMAZLARHOL]

thanks