Binomial theorem | Polynomial and rational functions | Algebra II | Khan Academy

[@andresleonardocastro5466]

"Let's just work through a few just to realize how quickly they get painful." How encouraging.

[@lelouchlamperouge3014]

Atleast he wasn't lying

[@maximcerta1641]

well he offered a solution

[@kaylingardner_]

just keeping it real😭

[@lukazade1]

subaru natsuki is real for this

[@harrison85]

Good luck w your math tests everyone, wishing you luck 🤘

[@thisisfrogx6808]

Harrison Hub mine’s tomorrow 😫

[@samaaalbaik]

Thanks!!! Good luck to u as well💛

[@alvincua4142]

Thanks I got an A 🌟

[@monighosh6639]

ভর্তিযুদ্ধে তোমাদের প্রস্তুতিকে শাণিত করতে জয়কলি পরিবারের ধারাবাহিক shortcut video থাকছে বিভিন্ন অধ্যায় এর উপর।আমাদের ভিডিও দেখতে নিচের লিঙ্কে ক্লিক করুন । kzbin.info/www/bejne/eaq6fGaMZ9x2sLM

[@joshuastory7265]

Thanks

[@Bottle502]

This guy has a great voice

[@izmasafa9582]

You are absolutely right.

[@peterkim994]

Lowkey, he is 3Blue1Brown

[@oscarstill909]

@@peterkim994 HE IS NOT 3BLUE 1 BROWN he is Sal Khan who is the head & founder of the Khan academy which is an online/internet and also and international organisation which teaches students from the kindergarten grädë to the yr 12 grade! So there u go❕❕‼️‼️‼️also I would HIGHLY RECOMMEND AND STRONGLY RECOMMEND THEIR CLIPS THEY WILL FIX YOUR EDUCATIONAL WORLD 🌎 🆙

[@spidystrac6218]

Waste voice

[@FatimaZahra-zw8hh]

Agree 😅

[@ellispaulk878]

I don't know why I'm paying for college when youtube educators are way better teachers than the professors at my university.

[@AR-vb4xy]

Where you from?

[@damijinadu4184]

Lol, I have to learn this and I'm just in the 9th grade 😭

[@seanammielantonio6386]

.

[@mariomario-ih6mn]

@@damijinadu4184 I'm 12

[@ikeokyere3133]

They take their time to explain things for us to understand unlike university lecturers

[@alexdashkoff8583]

thank you for explaining this to me like a 4 yr old. It's these kind of explanations that I need. In my probability theory class, my prof just skimmed over the formula and expected us to understand what it meant

[@MicahDaRhuler]

bruh what kind of 4 year old's have you been hanging with?

[@existentialrap521]

Learn this well, children. I'm in graduate school right now and we're using this in probability class. Had to get a good refresher. The more time you take to learn content when you're younger, the easier life will be.

[@thomasbekkering]

After 2 years of not understanding a thing, this video explained it to me in 13 minutes. That moment when youtube teachers are better than High School teachers.

[@zhenix4616]

Wait you learn this in high school too i am in 8th Grade in Germany and i rivised this 3times

[@muhammadhasanshaikhyuyings244]

I feel u

[@IntenseNoobFPS]

this is like maths ASMR

[@monighosh6639]

ভর্তিযুদ্ধে তোমাদের প্রস্তুতিকে শাণিত করতে জয়কলি পরিবারের ধারাবাহিক shortcut video থাকছে বিভিন্ন অধ্যায় এর উপর।আমাদের ভিডিও দেখতে নিচের লিঙ্কে ক্লিক করুন । kzbin.info/www/bejne/eaq6fGaMZ9x2sLM

[@jaesguerra]

I just did myself a discouraging slap to the brain. 0:49

[@RimazAboelgasim]

Jecille Esguerra yah I did skull dissection too to give myself a lovely slap on the brain ;)

[@PallaviAcharya]

😂😂😂😂

[@randynguyen2020]

Thank you, 3 minutes into the video and I understand more than what my teacher lectured for 30 minutes.

[@danielcliffgonmei9050]

Y would ur teacher take 30 mins .....

[@prashamjain3635]

true as heaven

[@nicolettakouris]

​@@danielcliffgonmei9050teacher probably had to deal with multiple disruptions. 🙄

[@help7456]

“if we say n choose k we remember from combinatorics this would be equal to...” no sir actually we do not remember

[@Nicole_brume]

Frr period

[@biscuit5359]

Combinatorics is literally just the usage of the formula of Combination.

[@abdullahjaved2832]

Is illuminati a real thing? Khan: Let me colour code this.

[@zhenix4616]

Colour Cote Not Code

[@RabanyMedo]

@@zhenix4616 No it is color code.

[@Jasmineaq]

@@zhenix4616 Lol, it is code. It is hilarious when people try to depict themselves as smart by correcting others but get it wrong themselves

[@nishyanthkumar]

@@zhenix4616 r/confidentlyincorrect

[@CrimsonShoryuken]

I have a test in 2 hrs, thanks!

[@user-xx5nk1wv1e]

Hope you did great :) I'm going to do an exam (this is included) in about 12.

[@viewing-p2s]

@ i wonder what he is doing now?

[@jett6865]

So how's life ever since that math test LOL

[@akarshsharma2870]

It's been five years but student around the world are carrying forward your legacy of living on the edge

[@milam9667]

raymond lay remember this. You still alive?

[@Redmi10Asss]

I almost lost hope to understand this until I bumped into this video. Can't thank u enough❤

[@syedaghaliaali3400]

Wow...... for the first time I understand anything in maths this deeply...... It just sticked in the bottom of my brain....... Thank You so much Sir now I will never forget Binomial Theorum in my life thanks to you...... 👌

[@eduardorodriguez-oj3zc]

Finally I got it I got it Much appreciated sir

[@ianwalniuk9757]

These videos are highly invaluable and are far more concise than most material that you can find online. Thank you for your work, Sal. :)

[@wiv_pro]

Thank you, I’m having a presentation on this and I didn’t know a lot before I watched this video, but after I watched it and analyzed it I understood most of it thank you. :)

[@teentalex]

I was lost since the beginning

[@imbrand5040]

the first few minutes were fine then he went to actual binomial theorem part and now my brain hurts

[@joshvir262]

Rev limits harsh

[@zuro181]

@Rev limits Wow that's harsh :(

[@hco4203]

@Random Autonomous Drone Pilot not cool

[@lotheeu2087]

@Random Autonomous Drone Pilot lmao ig im dumb too then

[@sigmabond1289]

its such a relief to get sal on another video...he usually doesn't teach maths....coz I never hv trouble understanding what he teaches...the best teacher ever..

[@Slayer_Abbyss]

Khan: "This comes straight out of combinatorics" Me: "Straight out of Compton"

[@qhansen123]

this literally saved my life i have a math 30-1 diploma tomorrow (Canadian) and i couldn't sit down and do it from a book. we don't use the sum notation but it's the same thing and much easier.

[@himalrana4177]

Thanks for helping me to understand the binomial theorem ,sir!!!

[@mercypeters7913]

I was about to change my course, because of maths, especially because of the topic binomial, but right now I think I'll give it a rethink

[@Studentoflife-x2d]

Hope after rethinking you made the right choice

[@comradesalman7625]

Its been 7 years. I dont think he is gonna answer you.​@@Studentoflife-x2d

[@pixelblaze8284]

great job you really saved me

[@helloitsfire]

been 7 years but still helping many people by this video.

[@om_unique]

Thank you. Black background with colourful text is amazing.

[@reddy_b_official]

This is the best explained way of teaching this topic

[@TheDinobam]

i love how the video takes as long as it does just because of the color switching, meaning their explanation could be done in less time. i love the effort you guys put into these videos

[@prashamjain3635]

oh god thank you , you just came in like a saviour. Our school was teaching us this chapter without teaching permutation combination and we had no clue but you came in and explained it so easily omg thank you .

[@roberthuff3122]

🎯 Key Takeaways for quick navigation: 00:00 🧮 *Introduction to binomial theorem* - Introductory concept of taking higher powers of binomials, and how it could get complex. - Several basic examples provided, from a + b to the 0 power, up to a + b to the 3rd power. 03:21 🗒 *Explanation of binomial theorem* - Binomial theorem introduced as a solution to simplify calculations with higher powers. - Binomial theorem formula explained and broken down for easier understanding. 06:13 🛠 *Application of binomial theorem* - Demonstrative example of a + b to the 4th power using the binomial theorem. - Process of calculating factorials further broken down to identify coefficients. - Application of the theorem results in an expanded form of a binomial to the 4th power. 12:31 🔄 *Symmetry in binomial theorem* - Identification of a pattern or symmetry in the results, showing how coefficients and powers of variables decrease and increase symmetrically. - Overview of longer explanations and examples to be covered in future sessions. Made with HARPA AI

[@PrudentialViews]

Can we just appreciate how he has to continue doing this math and switching colors at the same time

[@Ou_dembele]

when i used to learn algebra at the start the notations seemed scary but after i started watching khan academy it helped me understand what those notations mean.

[@kira1995]

You, sir, have some kind of magic. I'm not sure what it is, but you have the ability to make things make sense. It's like you cast Comprehend Languages or something like that. Bless you.

[@mrinalinighosh9573]

this is amazing! so helpful I was lost before but then I replayed it and it finally made sense just phenomenal

[@zobayerabdullah27]

Thank you very much. Now I understand what binomial theorem is

[@Ibrahim-xq1wk]

Salman khan, you’re a hero for me and my 7th grade friends in algebra 2, we are gonna school these sophomores!!

[@Kurashiro1963]

The best teacher ever 👍🏻👍🏻

[@oureducationalhub2717]

Your way of teaching is awesome

[@mac7858]

Thanks. This tutorial helped me a great deal.

[@monighosh6639]

ভর্তিযুদ্ধে তোমাদের প্রস্তুতিকে শাণিত করতে জয়কলি পরিবারের ধারাবাহিক shortcut video থাকছে বিভিন্ন অধ্যায় এর উপর।আমাদের ভিডিও দেখতে নিচের লিঙ্কে ক্লিক করুন । kzbin.info/www/bejne/eaq6fGaMZ9x2sLM

[@georgeimmanuel4850]

The best teacher in the world. The pioneer of online education.

[@streetbadger4463]

WOWWWW! This man is a LEGEND ! respect to you sir , it is way easier when you look at it now compared to when I first viewed this video... Best wishes to this math prophet !!!

[@jaredwaters4293]

exactly what I needed to see, thanks. It was nice to see you take the time to explain every step.

[@wango6603]

I LOVE YOU AND I WILL BLESS YOUR ENTIRE BLOODLINE

[@Aba9846]

You're awesome bro. Keep up the good work!

[@spikespiegel9371]

Thank you khan!!!! I wish i could meet you in real life and shake your hand! You helped me and my wife, mori calliope, get through algebra 2 with ease!

[@LilCarl-pl6py]

my lecture never had time to take me through but you made it look better that way

[@smiley4634]

Truly earned my respect Hats off for this guy

[@GekiClaws]

This theorom is so complex! I can't believe people can remember it! FYI: I'm an 11 yr old student studying Algebra II.

[@MonkeyDLuffy-bp8ir]

You probably won't have to use it for a long time when it comes again ull learn it easily enough as long as you understood the concept

[@fllyziescwt]

I don't regret watching this video. 💯📹📹

[@bobbysepulveda9771]

Wow, my professor never even explained what n choose k meant. What would I do without khan academy!

[@lickidy_dickidy.4870]

I learnt this now i need to flex on everyone, i like it easy to learn

[@axeskull5193]

Could've just used Pascal's Triangle but that works too

[@mobpod420]

Not when you're raising a binomial to the power of 20 and you need to memorize the 21st level.

[@axeskull5193]

Hahaha yeah

[@wellwhatcanisay4489]

You can do 20Cx on the calculator though

[@maricaloubser6733]

Not when you're not allowed to use a calculator

[@imnotcrazyjustinsane9433]

@@wellwhatcanisay4489 except your welcome~

[@duke_jo]

God bless you

[@ZigZagGod]

This man is a godsend! Thank you so much Mr.Khan for making mine and so many other students lives so much easier, i cant thank you enough!

[@erick4908]

Listening to this guy is very relaxing and reassuring. It feels like he's telling you, "Relax, it doesn't make sense yet, but it will at the end."

[@veer8243]

I regret why I didn't pay attention to this channel during my school days 🥺, this is true gem 💎

[@mxrgxrtt]

Thanks.. This video helps a lot for me especially when our teacher doesn't teach at all.

[@uktuhilrechok4271]

its very useful to learn maths while improving your english

[@submissivekoala]

Idk about my classmates using the Pascal triangle but this is much more easier for me

[@elilivingston3802]

explains it very well thank you soo much

[@muhammadhasanshaikhyuyings244]

the first 6 minutes of this video taught me more than what my teacher taught my class for weeks on end.

[@sujonahamed556]

what a nice trick is this. I don't forget this formula.. Thanks a lot sir for making such these type of tutorial

[@zooiii7113]

Oh my goodness i understand! Thank you!

[@azeezaz7729]

in my whole years of highschool , khan academy never failed me

[@graceychia6805]

For the first time in history I've understood well something in maths ...

[@aishusuresh1798]

man you teach so good

[@ChloeMukibi]

This is a lifesaver! Thank you!

[@raebanzuela]

12:14 you should get him a glass of water hahaha. like if you also notice that lmao.

[@ShivaPrasad-hm5lk]

lmao means what bro😑

[@kendytchin8897]

Thanks i really needed this. Your explanation was really easy to grasp. Thanks again💓😤

[@TechAmbition]

Maaaan This Explanation is 🔥

[@cockerala1633]

How can express my thanks... Thank you very much sir......... God bless you

[@jagannathnandy873]

ITS CLEAR AND EASY TO UNDERSTAND

[@gm2407]

When you have to come here from a mind your decisions video to understand the proof demonstration of why pie is less than 22/7. Also thank you this makes so much more sense as to where someone would get a really long binomial from.

[@harryk1126]

A blessing to mankind

[@medievalmusiclover]

You are a natural Professor! Thank You Sal.

[@amd.35]

Matthew 19:26 With God all things are possible

[@scar-kq3cl]

this is so much better than the plain old and boring The Organic Chemistry Tutor channel

[@blackmotion8297]

Thanks you so much bro this helps me a lots

[@amd.35]

Mark 11:24 says, "Therefore I tell you, whatever you ask in prayer, believe that you have received it, and it will be yours".

[@neethugeorge5079]

It's very easy to understand.. ✌✌👍👍👍

[@yashuppot3214]

This makes the power rule for deriviatives make so much more sense thank you so much

[@aadityatripathi9284]

BRO IS DOING LOT OF HARD WORK in changing colors

[@ruthmcevoy8300]

Amazingly helpful video. Thank you.

[@maximcerta1641]

really well explained! i understood everything. Thanks a lot

[@AlessandroZir]

thanks! ❤️🙏🙌

[@krsureka6549]

After a very long gap...I watch this video..😅😅 However awesome...

[@falahmshali6158]

Khan Akademy is The Best Channel On KZbin!

[@eatwater3282]

I'm in the 10th grade, and I learned more in this video than I ever had in my school.

[@hindiurmilamaam5518]

I m from india this video is very helpful

[@sophiecoorey5099]

I'm currently in year 11 (Aus) in isolation, ngl this was great thank you muchly

[@Khontadhondato]

I’m really poor at math, so this was a lil confusing to me, but I understood it with your great examples. It soo after seemed easy, and correct me if I’m wrong, but this kind of reminds me of the narrative, or resolving methods of limits.

[@gadremiebeats7530]

Wow I finally understand this Thanks Alot

[@Touch-me-not-Muni]

Gud understanding... Thnk u a lot sir

[@zukisanimakapela9055]

You are incredible, greatly appreciated sir! Awesome explanation, please keep it up!

[@Rayce001]

I’m preparing for my first year in the university as a student of mechanical engineering and I found your channel❤️

[@mantubeyou9350]

thank you khan acdemy

[@coltgad4411]

thanks you for high level AA you are my youtue teacher

[@itumelengramatlo1899]

The voice makes you pay attention attentivelyB-)

[@iExplorer64]

Thank you so much, this helped me a lot