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

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  • Опубліковано 15 гру 2024

КОМЕНТАРІ • 666

  • @andresleonardocastro5466
    @andresleonardocastro5466 3 роки тому +785

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

  • @harrison85
    @harrison85 5 років тому +930

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

    • @thisisfrogx6808
      @thisisfrogx6808 5 років тому +8

      Harrison Hub mine’s tomorrow 😫

    • @samaaalbaik
      @samaaalbaik 5 років тому +5

      Thanks!!! Good luck to u as well💛

    • @alvincua4142
      @alvincua4142 5 років тому +4

      Thanks
      I got an A 🌟

    • @monighosh6639
      @monighosh6639 4 роки тому

      ভর্তিযুদ্ধে তোমাদের প্রস্তুতিকে শাণিত করতে জয়কলি পরিবারের ধারাবাহিক shortcut video থাকছে বিভিন্ন অধ্যায় এর উপর।আমাদের ভিডিও দেখতে নিচের লিঙ্কে ক্লিক করুন । ua-cam.com/video/CyWK3V2wCzQ/v-deo.html

    • @joshuastory7265
      @joshuastory7265 4 роки тому +1

      Thanks

  • @Bottle502
    @Bottle502 8 років тому +477

    This guy has a great voice

    • @izmasafa9582
      @izmasafa9582 4 роки тому +11

      You are absolutely right.

    • @peterkim994
      @peterkim994 4 роки тому +4

      Lowkey, he is 3Blue1Brown

    • @oscarstill909
      @oscarstill909 3 роки тому +10

      @@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
      @spidystrac6218 3 роки тому +1

      Waste voice

    • @FatimaZahra-zw8hh
      @FatimaZahra-zw8hh 2 місяці тому

      Agree 😅

  • @ellispaulk878
    @ellispaulk878 5 років тому +1843

    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
      @AR-vb4xy 5 років тому +6

      Where you from?

    • @damijinadu4184
      @damijinadu4184 5 років тому +91

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

    • @seanammielantonio6386
      @seanammielantonio6386 5 років тому +2

      .

    • @mariomario-ih6mn
      @mariomario-ih6mn 5 років тому +18

      @@damijinadu4184 I'm 12

    • @ikeokyere3133
      @ikeokyere3133 5 років тому +25

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

  • @alexdashkoff8583
    @alexdashkoff8583 3 роки тому +125

    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
      @MicahDaRhuler Рік тому +22

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

  • @IntenseNoobFPS
    @IntenseNoobFPS 7 років тому +102

    this is like maths ASMR

    • @monighosh6639
      @monighosh6639 4 роки тому +2

      ভর্তিযুদ্ধে তোমাদের প্রস্তুতিকে শাণিত করতে জয়কলি পরিবারের ধারাবাহিক shortcut video থাকছে বিভিন্ন অধ্যায় এর উপর।আমাদের ভিডিও দেখতে নিচের লিঙ্কে ক্লিক করুন । ua-cam.com/video/CyWK3V2wCzQ/v-deo.html

  • @thomasbekkering
    @thomasbekkering 4 роки тому +56

    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.

  • @existentialrap521
    @existentialrap521 2 роки тому +20

    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.

  • @abdullahjaved2832
    @abdullahjaved2832 5 років тому +187

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

    • @zhenix4616
      @zhenix4616 3 роки тому

      Colour Cote Not Code

    • @RabanyMedo
      @RabanyMedo 3 роки тому +6

      @@zhenix4616 No it is color code.

    • @Jasmineaq
      @Jasmineaq 2 роки тому +6

      @@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
      @nishyanthkumar 2 роки тому +1

      @@zhenix4616 r/confidentlyincorrect

  • @randynguyen2020
    @randynguyen2020 6 років тому +105

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

  • @help7456
    @help7456 4 роки тому +52

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

    • @Nicole_brume
      @Nicole_brume 8 місяців тому +1

      Frr period

    • @biscuit5359
      @biscuit5359 3 місяці тому +1

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

  • @jaesguerra
    @jaesguerra 7 років тому +331

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

    • @RimazAboelgasim
      @RimazAboelgasim 7 років тому +31

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

    • @PallaviAcharya
      @PallaviAcharya 6 років тому +3

      😂😂😂😂

  • @CrimsonShoryuken
    @CrimsonShoryuken 10 років тому +176

    I have a test in 2 hrs, thanks!

    • @user-xx5nk1wv1e
      @user-xx5nk1wv1e 9 років тому +3

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

    • @viewing-p2s
      @viewing-p2s 5 років тому +1

      @ i wonder what he is doing now?

    • @jett6865
      @jett6865 5 років тому +6

      So how's life ever since that math test LOL

    • @akarshsharma2870
      @akarshsharma2870 4 роки тому +6

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

    • @milam9667
      @milam9667 4 роки тому

      raymond lay remember this. You still alive?

  • @Redmi10Asss
    @Redmi10Asss 9 місяців тому +2

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

  • @teentalex
    @teentalex 9 років тому +188

    I was lost since the beginning

    • @imbrand5040
      @imbrand5040 5 років тому +14

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

    • @joshvir262
      @joshvir262 5 років тому +3

      Rev limits harsh

    • @zuro181
      @zuro181 5 років тому +20

      @Rev limits Wow that's harsh :(

    • @hco4203
      @hco4203 4 роки тому +8

      @Random Autonomous Drone Pilot not cool

    • @lotheeu2087
      @lotheeu2087 4 роки тому

      @Random Autonomous Drone Pilot lmao ig im dumb too then

  • @Slayer_Abbyss
    @Slayer_Abbyss 3 роки тому +14

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

  • @eduardorodriguez-oj3zc
    @eduardorodriguez-oj3zc 10 років тому +14

    Finally
    I got it
    I got it
    Much appreciated sir

  • @ianwalniuk9757
    @ianwalniuk9757 7 років тому +9

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

  • @syedaghaliaali3400
    @syedaghaliaali3400 Рік тому +3

    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......
    👌

  • @sigmabond1289
    @sigmabond1289 7 років тому +2

    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..

  • @wiv_pro
    @wiv_pro 2 роки тому +8

    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. :)

  • @mercypeters7913
    @mercypeters7913 7 років тому +25

    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
      @Studentoflife-x2d Місяць тому

      Hope after rethinking you made the right choice

    • @comradesalman7625
      @comradesalman7625 Місяць тому

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

  • @pixelblaze8284
    @pixelblaze8284 8 років тому +10

    great job you really saved me

  • @himalrana4177
    @himalrana4177 8 років тому +7

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

  • @helloitsfire
    @helloitsfire 3 роки тому +3

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

  • @om_unique
    @om_unique 7 років тому +27

    Thank you. Black background with colourful text is amazing.

  • @qhansen123
    @qhansen123 8 років тому +2

    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.

  • @prashamjain3635
    @prashamjain3635 3 роки тому +8

    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 .

  • @reddy_b_official
    @reddy_b_official 5 місяців тому +1

    This is the best explained way of teaching this topic

  • @PrudentialViews
    @PrudentialViews 2 роки тому +2

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

  • @mac7858
    @mac7858 9 років тому +6

    Thanks. This tutorial helped me a great deal.

    • @monighosh6639
      @monighosh6639 4 роки тому

      ভর্তিযুদ্ধে তোমাদের প্রস্তুতিকে শাণিত করতে জয়কলি পরিবারের ধারাবাহিক shortcut video থাকছে বিভিন্ন অধ্যায় এর উপর।আমাদের ভিডিও দেখতে নিচের লিঙ্কে ক্লিক করুন । ua-cam.com/video/CyWK3V2wCzQ/v-deo.html

  • @TheDinobam
    @TheDinobam Рік тому

    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

  • @axeskull5193
    @axeskull5193 8 років тому +38

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

    • @mobpod420
      @mobpod420 8 років тому +55

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

    • @axeskull5193
      @axeskull5193 8 років тому

      Hahaha yeah

    • @wellwhatcanisay4489
      @wellwhatcanisay4489 7 років тому

      You can do 20Cx on the calculator though

    • @maricaloubser6733
      @maricaloubser6733 6 років тому +9

      Not when you're not allowed to use a calculator

    • @imnotcrazyjustinsane9433
      @imnotcrazyjustinsane9433 6 років тому +5

      @@wellwhatcanisay4489 except your welcome~

  • @duke_jo
    @duke_jo 2 місяці тому +1

    God bless you

  • @wango6603
    @wango6603 2 роки тому +1

    I LOVE YOU AND I WILL BLESS YOUR ENTIRE BLOODLINE

  • @georgeimmanuel4850
    @georgeimmanuel4850 4 роки тому

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

  • @Aba9846
    @Aba9846 6 років тому +3

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

  • @oureducationalhub2717
    @oureducationalhub2717 3 роки тому

    Your way of teaching is awesome

  • @Ou_dembele
    @Ou_dembele 3 роки тому

    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.

  • @mrinalinighosh9573
    @mrinalinighosh9573 8 років тому +3

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

  • @GekiClaws
    @GekiClaws 8 років тому +1

    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
      @MonkeyDLuffy-bp8ir 7 років тому +1

      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

  • @roberthuff3122
    @roberthuff3122 10 місяців тому

    🎯 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

  • @Ibrahim-xq1wk
    @Ibrahim-xq1wk 5 років тому

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

  • @erick4908
    @erick4908 5 років тому +1

    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."

  • @azeezaz7729
    @azeezaz7729 3 роки тому +1

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

  • @jaredwaters4293
    @jaredwaters4293 7 років тому +1

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

  • @Kurashiro1963
    @Kurashiro1963 Рік тому

    The best teacher ever 👍🏻👍🏻

  • @kira1995
    @kira1995 3 роки тому

    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.

  • @submissivekoala
    @submissivekoala 5 років тому +2

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

  • @muhammadhasanshaikhyuyings244

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

  • @lickidy_dickidy.4870
    @lickidy_dickidy.4870 4 роки тому +2

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

  • @LilCarl-pl6py
    @LilCarl-pl6py 8 місяців тому

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

  • @fllyziescwt
    @fllyziescwt 2 роки тому

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

  • @smiley4634
    @smiley4634 2 роки тому

    Truly earned my respect
    Hats off for this guy

  • @piusadas2220
    @piusadas2220 4 роки тому +2

    Who else is solving number theory books all by themselves and these wonderful teachers are life??

  • @jaanchaudhry1682
    @jaanchaudhry1682 4 роки тому +2

    Watching in class

  • @graceychia6805
    @graceychia6805 2 роки тому

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

  • @veer8243
    @veer8243 Рік тому

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

  • @scar-kq3cl
    @scar-kq3cl Рік тому

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

  • @spikespiegel9371
    @spikespiegel9371 Рік тому

    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!

  • @bobbysepulveda9771
    @bobbysepulveda9771 2 роки тому

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

  • @streetbadger4463
    @streetbadger4463 3 роки тому

    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 !!!

  • @ChloeMukibi
    @ChloeMukibi Рік тому

    This is a lifesaver! Thank you!

  • @ruthmcevoy8300
    @ruthmcevoy8300 Рік тому

    Amazingly helpful video. Thank you.

  • @harryk1126
    @harryk1126 6 років тому

    A blessing to mankind

  • @raebanzuela
    @raebanzuela 7 років тому +3

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

  • @ZigZagGod
    @ZigZagGod 6 років тому

    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!

  • @aishusuresh1798
    @aishusuresh1798 Рік тому

    man you teach so good

  • @medievalmusiclover
    @medievalmusiclover 7 років тому

    You are a natural Professor! Thank You Sal.

  • @aadityatripathi9284
    @aadityatripathi9284 2 місяці тому

    BRO IS DOING LOT OF HARD WORK in changing colors

  • @jagannathnandy873
    @jagannathnandy873 7 років тому

    ITS CLEAR AND EASY TO UNDERSTAND

  • @mxrgxrtt
    @mxrgxrtt 6 років тому

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

  • @scorpion2070
    @scorpion2070 3 роки тому

    faleminderit

  • @uktuhilrechok4271
    @uktuhilrechok4271 7 років тому

    its very useful to learn maths while improving your english

  • @eatwater3282
    @eatwater3282 2 місяці тому

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

  • @elilivingston3802
    @elilivingston3802 5 місяців тому

    explains it very well thank you soo much

  • @zooiii7113
    @zooiii7113 Рік тому

    Oh my goodness i understand! Thank you!

  • @abhi20user-z8jm5my9p
    @abhi20user-z8jm5my9p 4 роки тому +2

    Is there any trinomial theorem

  • @kingarth0r
    @kingarth0r 8 років тому +6

    0 to the 0 is one because of this law

  • @gm2407
    @gm2407 3 роки тому

    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.

  • @falahmshali6158
    @falahmshali6158 5 років тому

    Khan Akademy is The Best Channel On UA-cam!

  • @TechAmbition
    @TechAmbition 7 місяців тому

    Maaaan This Explanation is 🔥

  • @cockerala1633
    @cockerala1633 5 років тому

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

  • @itumelengramatlo1899
    @itumelengramatlo1899 4 роки тому +2

    The voice makes you pay attention attentivelyB-)

  • @blackmotion8297
    @blackmotion8297 2 роки тому

    Thanks you so much bro this helps me a lots

  • @sujonahamed556
    @sujonahamed556 3 роки тому

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

  • @yashuppot3214
    @yashuppot3214 5 років тому

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

  • @kendytchin8897
    @kendytchin8897 2 роки тому

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

  • @maximcerta1641
    @maximcerta1641 2 роки тому

    really well explained! i understood everything. Thanks a lot

  • @iExplorer64
    @iExplorer64 6 років тому +1

    Thank you so much, this helped me a lot

  • @s.a.4397
    @s.a.4397 9 місяців тому

    Thank you! Awesome!!

  • @krsureka6549
    @krsureka6549 3 роки тому

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

  • @neethugeorge5079
    @neethugeorge5079 5 років тому

    It's very easy to understand.. ✌✌👍👍👍

  • @danielhiggins4331
    @danielhiggins4331 2 роки тому

    HE MAY FINALLY ANSWER THE QUESTION ... BUT LIKE ALL TA'S EVER ... HE'S WAY MORE INTERESTED IN SHOWING YOU THE DEPTH OF HIS ARCANE LORE THAN HE IS ABOUT TEACHING YOU THE KNOWLEDGE!!

    • @rmdir
      @rmdir 2 роки тому +1

      It's not "arcane lore", he is trying to get you interested and thinking about process behind all this. Solving problems on your own (and understanding why), rather than just following rote mechanical steps to reach an answer.
      The modern Western education system teaches you how to pass tests, Khan (and others) are trying to actually teach you the material, which may seem particularly jarring if you spent a lifetime in indoctrination.

    • @Logan-zf1ft
      @Logan-zf1ft 2 роки тому

      @@rmdir you're ignorant

  • @Touch-me-not-Muni
    @Touch-me-not-Muni 6 років тому

    Gud understanding... Thnk u a lot sir

  • @kurtl.3773
    @kurtl.3773 7 років тому

    You explained it better in 13 minutes than my teacher in days

  • @satyajeetarya7790
    @satyajeetarya7790 6 років тому

    You r solving our concept... Fantastically.. Good job thanks for this video

  • @zukisanimakapela9055
    @zukisanimakapela9055 10 років тому +1

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

  • @burhanudin8687
    @burhanudin8687 3 роки тому

    Thank you very much, this is what i need

  • @mantubeyou9350
    @mantubeyou9350 8 років тому

    thank you khan acdemy