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

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  • čas přidán 25. 03. 2014
  • Practice this lesson yourself on KhanAcademy.org right now:
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    Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
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Komentáře • 648

  • @andresleonardocastro5466
    @andresleonardocastro5466 Před 3 lety +697

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

  • @harrison85
    @harrison85 Před 5 lety +879

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

    • @thisisfrogx6808
      @thisisfrogx6808 Před 5 lety +8

      Harrison Hub mine’s tomorrow 😫

    • @samaaalbaik
      @samaaalbaik Před 4 lety +5

      Thanks!!! Good luck to u as well💛

    • @alvincua4142
      @alvincua4142 Před 4 lety +4

      Thanks
      I got an A 🌟

    • @monighosh6639
      @monighosh6639 Před 4 lety

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

    • @joshuastory7265
      @joshuastory7265 Před 3 lety +1

      Thanks

  • @ellispaulk878
    @ellispaulk878 Před 5 lety +1761

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

  • @Bottle502
    @Bottle502 Před 7 lety +446

    This guy has a great voice

    • @izmasafa9582
      @izmasafa9582 Před 4 lety +11

      You are absolutely right.

    • @peterkim994
      @peterkim994 Před 3 lety +4

      Lowkey, he is 3Blue1Brown

    • @oscarstill909
      @oscarstill909 Před 3 lety +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 Před 3 lety +1

      Waste voice

  • @alexdashkoff8583
    @alexdashkoff8583 Před 3 lety +107

    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 Před rokem +17

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

  • @help7456
    @help7456 Před 3 lety +46

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

  • @jaesguerra
    @jaesguerra Před 6 lety +326

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

    • @RimazAboelgasim
      @RimazAboelgasim Před 6 lety +31

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

    • @PallaviAcharya
      @PallaviAcharya Před 5 lety +3

      😂😂😂😂

  • @abdullahjaved2832
    @abdullahjaved2832 Před 4 lety +183

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

    • @zhenix4616
      @zhenix4616 Před 2 lety

      Colour Cote Not Code

    • @RabanyMedo
      @RabanyMedo Před 2 lety +6

      @@zhenix4616 No it is color code.

    • @Jasmineaq
      @Jasmineaq Před 2 lety +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 Před 2 lety +1

      @@zhenix4616 r/confidentlyincorrect

  • @thomasbekkering
    @thomasbekkering Před 3 lety +50

    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.

  • @IntenseNoobFPS
    @IntenseNoobFPS Před 7 lety +97

    this is like maths ASMR

    • @monighosh6639
      @monighosh6639 Před 4 lety +2

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

  • @existentialrap521
    @existentialrap521 Před rokem +15

    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.

  • @randynguyen2020
    @randynguyen2020 Před 6 lety +105

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

  • @teentalex
    @teentalex Před 8 lety +189

    I was lost since the beginning

    • @reese-794
      @reese-794 Před 5 lety +8

      ur not alone

    • @imbrand5040
      @imbrand5040 Před 4 lety +14

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

    • @joshvir262
      @joshvir262 Před 4 lety +3

      Rev limits harsh

    • @zuro181
      @zuro181 Před 4 lety +20

      @Rev limits Wow that's harsh :(

    • @hco4203
      @hco4203 Před 4 lety +8

      @Random Autonomous Drone Pilot not cool

  • @CrimsonShoryuken
    @CrimsonShoryuken Před 9 lety +176

    I have a test in 2 hrs, thanks!

    • @user-xx5nk1wv1e
      @user-xx5nk1wv1e Před 9 lety +3

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

    • @DeZiar
      @DeZiar Před 5 lety +1

      @ i wonder what he is doing now?

    • @jett6865
      @jett6865 Před 4 lety +6

      So how's life ever since that math test LOL

    • @akarshsharma2870
      @akarshsharma2870 Před 4 lety +6

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

    • @milam9667
      @milam9667 Před 4 lety

      raymond lay remember this. You still alive?

  • @Slayer_Abbyss
    @Slayer_Abbyss Před 3 lety +13

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

  • @user-jn3dn4ss2i
    @user-jn3dn4ss2i Před 5 měsíci +2

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

  • @ianwalniuk9757
    @ianwalniuk9757 Před 7 lety +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. :)

  • @mercypeters7913
    @mercypeters7913 Před 6 lety +23

    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

  • @eduardorodriguez-oj3zc
    @eduardorodriguez-oj3zc Před 10 lety +14

    Finally
    I got it
    I got it
    Much appreciated sir

  • @wiv_pro
    @wiv_pro Před 2 lety +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. :)

  • @mrinalinighosh9573
    @mrinalinighosh9573 Před 8 lety +3

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

  • @sigmabond1289
    @sigmabond1289 Před 7 lety +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..

  • @jaredwaters4293
    @jaredwaters4293 Před 6 lety +1

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

  • @qhansen123
    @qhansen123 Před 8 lety +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.

  • @himalrana4177
    @himalrana4177 Před 7 lety +7

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

  • @syedaghaliaali3400
    @syedaghaliaali3400 Před rokem +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......
    👌

  • @10ksubswithoutoriginalcont65

    0:45 😂😂 only reason i watch sal's videos

  • @pixelblaze8284
    @pixelblaze8284 Před 8 lety +10

    great job you really saved me

  • @PrudentialViews
    @PrudentialViews Před rokem +2

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

  • @helloitsfire
    @helloitsfire Před 3 lety +3

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

  • @zukisanimakapela9055
    @zukisanimakapela9055 Před 10 lety +1

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

  • @kira1995
    @kira1995 Před 3 lety

    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.

  • @ZigZagGod
    @ZigZagGod Před 6 lety

    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!

  • @streetbadger4463
    @streetbadger4463 Před 3 lety

    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 !!!

  • @tylerdipietro4201
    @tylerdipietro4201 Před 7 lety

    This is very complicated but I get it now and I love it. Thank you Sal!!!

  • @Adam-qg8yt
    @Adam-qg8yt Před 8 měsíci

    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

  • @sanchezchris95
    @sanchezchris95 Před 9 lety

    Khan Great as always thank you so much! You are doing the world good with all your amazing videos. I can't thank you enough.

  • @cockerala1633
    @cockerala1633 Před 5 lety

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

  • @axeskull5193
    @axeskull5193 Před 8 lety +38

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

  • @Ou_dembele
    @Ou_dembele Před 3 lety

    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.

  • @yashuppot3214
    @yashuppot3214 Před 4 lety

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

  • @abdallahkalthoum8255
    @abdallahkalthoum8255 Před 9 lety

    thank you a lot,this saved me just right before the test day.

  •  Před 10 lety +1

    Great explanation. Thank you so much.

  • @sandrasilva-uo1ui
    @sandrasilva-uo1ui Před 4 lety

    Tremendous, excellent explanation, thank you, very much. God bless you tremendously. Thanks

  • @medievalmusiclover
    @medievalmusiclover Před 6 lety

    You are a natural Professor! Thank You Sal.

  • @Aba9846
    @Aba9846 Před 6 lety +3

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

  • @Ibrahim-xq1wk
    @Ibrahim-xq1wk Před 5 lety

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

  • @om_unique
    @om_unique Před 6 lety +27

    Thank you. Black background with colourful text is amazing.

  • @swetanjalisamal2792
    @swetanjalisamal2792 Před 6 lety +1

    Thank you so much.
    It was really helpful.

  • @prashamjain3635
    @prashamjain3635 Před 2 lety +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 .

  • @raebanzuela5860
    @raebanzuela5860 Před 6 lety +3

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

  • @gcmr87
    @gcmr87 Před 9 lety

    Yes. This is amazing!

  • @mac7858
    @mac7858 Před 9 lety +6

    Thanks. This tutorial helped me a great deal.

    • @monighosh6639
      @monighosh6639 Před 4 lety

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

  • @iExplorer64
    @iExplorer64 Před 6 lety +1

    Thank you so much, this helped me a lot

  • @adityasaxena5651
    @adityasaxena5651 Před 8 lety

    really great explanation! Keep it up!

  • @vanithaas.krishnan9822

    so imformative ..thnks alot ... amazing !!!

  • @mxrgxrtt
    @mxrgxrtt Před 5 lety

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

  • @maximcerta1641
    @maximcerta1641 Před rokem

    really well explained! i understood everything. Thanks a lot

  • @smiley4634
    @smiley4634 Před 2 lety

    Truly earned my respect
    Hats off for this guy

  • @reddy_b_official
    @reddy_b_official Před měsícem +1

    This is the best explained way of teaching this topic

  • @lickidy_dickidy.4870
    @lickidy_dickidy.4870 Před 4 lety +2

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

  • @gadremiebeats7530
    @gadremiebeats7530 Před 8 lety

    Wow
    I finally understand this
    Thanks Alot

  • @GekiClaws
    @GekiClaws Před 7 lety +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 Před 6 lety +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

  • @renewamulaudzi181
    @renewamulaudzi181 Před 4 lety

    this was very helpful thank you!

  • @azeezaz7729
    @azeezaz7729 Před 3 lety +1

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

  • @Spinomaks
    @Spinomaks Před 4 lety +2

    0:49 I gave myself such a slap that I became even more dysfunctional.

  • @ranveerjadhav928
    @ranveerjadhav928 Před rokem +1

    lovely explaination with easy understandable english

  • @yvonne3745
    @yvonne3745 Před 5 lety

    Omg u saved my life and troubles. I thank you

  • @sujonahamed556
    @sujonahamed556 Před 2 lety

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

  • @PuffleBuns
    @PuffleBuns Před 8 lety +42

    Sorry, just slapping myself on the wrist. . . Don't mind me.

    • @jef_f8751
      @jef_f8751 Před 4 lety +5

      People who put a squared plus b squared and forget the 2ab disgust me

  • @georgea.752
    @georgea.752 Před 7 lety

    Excellent! Thank you very much.

  • @hughjanus8450
    @hughjanus8450 Před 2 lety

    Very helpful, thank you!

  • @LilCarl-pl6py
    @LilCarl-pl6py Před 3 měsíci

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

  • @ngndnd
    @ngndnd Před 3 lety +5

    Idk why, but i like to teach myself the material BEFORE i start the class. I know i will fail if i follow along with the teacher.

  • @veer8243
    @veer8243 Před rokem

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

  • @user-zt8bv9ey1t
    @user-zt8bv9ey1t Před 11 měsíci

    This is a lifesaver! Thank you!

  • @georgeimmanuel4850
    @georgeimmanuel4850 Před 3 lety

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

  • @s.a.4397
    @s.a.4397 Před 5 měsíci

    Thank you! Awesome!!

  • @satyajeetarya7790
    @satyajeetarya7790 Před 5 lety

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

  • @Touch-me-not-Muni
    @Touch-me-not-Muni Před 5 lety

    Gud understanding... Thnk u a lot sir

  • @muhammadhasanshaikhyuyings244

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

  • @oureducationalhub2717
    @oureducationalhub2717 Před 2 lety

    Your way of teaching is awesome

  • @harryk1126
    @harryk1126 Před 5 lety

    A blessing to mankind

  • @kurtl.3773
    @kurtl.3773 Před 6 lety

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

  • @annieyang4763
    @annieyang4763 Před 6 měsíci +1

    Thank you! This is so helpful, I understand things so much more easily ;0

  • @kendytchin8897
    @kendytchin8897 Před rokem

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

  • @mr.ontological9583
    @mr.ontological9583 Před 9 lety +114

    Jesus how much did Sal smoke before making this video?

  • @piusadas2220
    @piusadas2220 Před 4 lety +2

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

  • @ruthmcevoy8300
    @ruthmcevoy8300 Před 7 měsíci

    Amazingly helpful video. Thank you.

  • @zooiii7113
    @zooiii7113 Před 8 měsíci

    Oh my goodness i understand! Thank you!

  • @jagannathnandy873
    @jagannathnandy873 Před 7 lety

    ITS CLEAR AND EASY TO UNDERSTAND

  • @elilivingston3802
    @elilivingston3802 Před měsícem

    explains it very well thank you soo much

  • @cabdixakiimmuxamed4930

    Thank you very much.i understand very well

  • @uktuhilrechok4271
    @uktuhilrechok4271 Před 6 lety

    its very useful to learn maths while improving your english

  • @submissivekoala
    @submissivekoala Před 5 lety +1

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

  • @blackmotion8297
    @blackmotion8297 Před 2 lety

    Thanks you so much bro this helps me a lots

  • @redpoka13
    @redpoka13 Před 3 lety

    I love how he uses the word 'painful' every time he mentions working out a solution because math simply is

  • @SarveshKumar-ml5jd
    @SarveshKumar-ml5jd Před 7 lety

    THAT WAS VERY NICE EXPLANATION

  • @anantabauri5366
    @anantabauri5366 Před rokem

    Nice explanation!

  • @Kurashiro1963
    @Kurashiro1963 Před 9 měsíci

    The best teacher ever 👍🏻👍🏻