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

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  • Опубліковано 25 бер 2014
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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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КОМЕНТАРІ • 649

  • @andresleonardocastro5466
    @andresleonardocastro5466 3 роки тому +699

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

  • @harrison85
    @harrison85 5 років тому +879

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

    • @thisisfrogx6808
      @thisisfrogx6808 5 років тому +8

      Harrison Hub mine’s tomorrow 😫

    • @samaaalbaik
      @samaaalbaik 4 роки тому +5

      Thanks!!! Good luck to u as well💛

    • @alvincua4142
      @alvincua4142 4 роки 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 3 роки тому +1

      Thanks

  • @ellispaulk878
    @ellispaulk878 5 років тому +1761

    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 +5

      Where you from?

    • @damijinadu4184
      @damijinadu4184 5 років тому +83

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

    • @seanammielantonio6386
      @seanammielantonio6386 4 роки тому +2

      .

    • @mariomario-ih6mn
      @mariomario-ih6mn 4 роки тому +17

      @@damijinadu4184 I'm 12

    • @ikeokyere3133
      @ikeokyere3133 4 роки тому +22

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

  • @Bottle502
    @Bottle502 7 років тому +447

    This guy has a great voice

    • @izmasafa9582
      @izmasafa9582 4 роки тому +11

      You are absolutely right.

    • @peterkim994
      @peterkim994 3 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

  • @alexdashkoff8583
    @alexdashkoff8583 3 роки тому +108

    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 +17

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

  • @jaesguerra
    @jaesguerra 6 років тому +326

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

    • @RimazAboelgasim
      @RimazAboelgasim 6 років тому +31

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

    • @PallaviAcharya
      @PallaviAcharya 5 років тому +3

      😂😂😂😂

  • @help7456
    @help7456 3 роки тому +46

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

  • @abdullahjaved2832
    @abdullahjaved2832 4 роки тому +183

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

    • @zhenix4616
      @zhenix4616 2 роки тому

      Colour Cote Not Code

    • @RabanyMedo
      @RabanyMedo 2 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

  • @existentialrap521
    @existentialrap521 Рік тому +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.

  • @thomasbekkering
    @thomasbekkering 3 роки тому +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 7 років тому +97

    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

  • @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.

  • @teentalex
    @teentalex 8 років тому +189

    I was lost since the beginning

    • @reese-794
      @reese-794 5 років тому +8

      ur not alone

    • @imbrand5040
      @imbrand5040 4 роки тому +14

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

    • @joshvir262
      @joshvir262 4 роки тому +3

      Rev limits harsh

    • @zuro181
      @zuro181 4 роки тому +20

      @Rev limits Wow that's harsh :(

    • @hco4203
      @hco4203 4 роки тому +8

      @Random Autonomous Drone Pilot not cool

  • @Slayer_Abbyss
    @Slayer_Abbyss 3 роки тому +13

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

  • @mercypeters7913
    @mercypeters7913 6 років тому +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

  • @user-jn3dn4ss2i
    @user-jn3dn4ss2i 5 місяців тому +2

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

  • @CrimsonShoryuken
    @CrimsonShoryuken 9 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 4 роки 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?

  • @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. :)

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

    Finally
    I got it
    I got it
    Much appreciated sir

  • @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. :)

  • @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.

  • @10ksubswithoutoriginalcont65
    @10ksubswithoutoriginalcont65 5 років тому +17

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

  • @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..

  • @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......
    👌

  • @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

  • @jaredwaters4293
    @jaredwaters4293 6 років тому +1

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

  • @PrudentialViews
    @PrudentialViews Рік тому +2

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

  • @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.

  • @himalrana4177
    @himalrana4177 7 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.

  • @Adam-qg8yt
    @Adam-qg8yt 8 місяців 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

  • @om_unique
    @om_unique 6 років тому +27

    Thank you. Black background with colourful text is amazing.

  • @raebanzuela5860
    @raebanzuela5860 6 років тому +3

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

  • @GekiClaws
    @GekiClaws 7 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 6 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

  • @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!

  • @tylerdipietro4201
    @tylerdipietro4201 7 років тому

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

  • @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 !!!

  • @mr.ontological9583
    @mr.ontological9583 9 років тому +114

    Jesus how much did Sal smoke before making this video?

    • @xxxexyz87
      @xxxexyz87 9 років тому +17

      carl sagan: "Bruhhh"

  • @pixelblaze8284
    @pixelblaze8284 8 років тому +10

    great job you really saved me

  • @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.

  • @prashamjain3635
    @prashamjain3635 2 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 .

  • @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!!

  • @axeskull5193
    @axeskull5193 8 років тому +38

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

    • @mobpod420
      @mobpod420 7 років тому +52

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

    • @axeskull5193
      @axeskull5193 7 років тому

      Hahaha yeah

    • @wellwhatcanisay4489
      @wellwhatcanisay4489 6 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 5 років тому +5

      @@wellwhatcanisay4489 except your welcome~

  • @yashuppot3214
    @yashuppot3214 4 роки тому

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

  • @zukisanimakapela9055
    @zukisanimakapela9055 10 років тому +1

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

  • @abdallahkalthoum8255
    @abdallahkalthoum8255 9 років тому

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

  • @cockerala1633
    @cockerala1633 5 років тому

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

  • @PuffleBuns
    @PuffleBuns 8 років тому +42

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

    • @jef_f8751
      @jef_f8751 4 роки тому +5

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

  • @medievalmusiclover
    @medievalmusiclover 6 років тому

    You are a natural Professor! Thank You Sal.

  • @mxrgxrtt
    @mxrgxrtt 5 років тому

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

  • @reddy_b_official
    @reddy_b_official Місяць тому +1

    This is the best explained way of teaching this topic

  • @sandrasilva-uo1ui
    @sandrasilva-uo1ui 4 роки тому

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

  • @veer8243
    @veer8243 Рік тому

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

  • @muhammadhasanshaikhyuyings244

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

  • @redpoka13
    @redpoka13 3 роки тому

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

  • @sanchezchris95
    @sanchezchris95 9 років тому

    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.

  • @azeezaz7729
    @azeezaz7729 3 роки тому +1

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

  • @stevewest6133
    @stevewest6133 4 роки тому

    Is the "longhand" binomial theorem really needed if you already know how to use Pascal's Triangle? The latter is much easier. And I'm trying to wrap my head around whether there are specific problems where Pascal's will not work.

  • @smiley4634
    @smiley4634 2 роки тому

    Truly earned my respect
    Hats off for this guy

  • @gadremiebeats7530
    @gadremiebeats7530 8 років тому

    Wow
    I finally understand this
    Thanks Alot

  •  10 років тому +1

    Great explanation. Thank you so much.

  • @gcmr87
    @gcmr87 9 років тому

    Yes. This is amazing!

  • @piusadas2220
    @piusadas2220 4 роки тому +2

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

  • @adityasaxena5651
    @adityasaxena5651 8 років тому

    really great explanation! Keep it up!

  • @vanithaas.krishnan9822
    @vanithaas.krishnan9822 7 років тому

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

  • @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

  • @iExplorer64
    @iExplorer64 6 років тому +1

    Thank you so much, this helped me a lot

  • @sujonahamed556
    @sujonahamed556 2 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

  • @kurtl.3773
    @kurtl.3773 6 років тому

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

  • @ranveerjadhav928
    @ranveerjadhav928 Рік тому +1

    lovely explaination with easy understandable english

  • @renewamulaudzi181
    @renewamulaudzi181 4 роки тому

    this was very helpful thank you!

  • @swetanjalisamal2792
    @swetanjalisamal2792 6 років тому +1

    Thank you so much.
    It was really helpful.

  • @ngndnd
    @ngndnd 3 роки тому +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.

    • @1973Ganesh
      @1973Ganesh 2 роки тому

      You just changed my life

  • @Aba9846
    @Aba9846 6 років тому +3

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

  • @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

  • @maximcerta1641
    @maximcerta1641 Рік тому

    really well explained! i understood everything. Thanks a lot

  • @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.

  • @georgeimmanuel4850
    @georgeimmanuel4850 3 роки тому

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

  • @Spinomaks
    @Spinomaks 4 роки тому +2

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

  • @VitaminDee
    @VitaminDee 5 років тому +6

    Give yourself a “gentle but not overly discouraging slap on the wrist” 😂😂😂

  • @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."

  • @hughjanus8450
    @hughjanus8450 2 роки тому

    Very helpful, thank you!

  • @submissivekoala
    @submissivekoala 5 років тому +1

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

  • @LilCarl-pl6py
    @LilCarl-pl6py 3 місяці тому

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

  • @georgea.752
    @georgea.752 7 років тому

    Excellent! Thank you very much.

  • @spikespiegel9371
    @spikespiegel9371 8 місяців 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!

  • @harryk1126
    @harryk1126 6 років тому

    A blessing to mankind

  • @yvonne3745
    @yvonne3745 5 років тому

    Omg u saved my life and troubles. I thank you

  • @oureducationalhub2717
    @oureducationalhub2717 2 роки тому

    Your way of teaching is awesome

  • @jagannathnandy873
    @jagannathnandy873 7 років тому

    ITS CLEAR AND EASY TO UNDERSTAND

  • @bobbysepulveda9771
    @bobbysepulveda9771 2 роки тому

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

  • @graceychia6805
    @graceychia6805 Рік тому

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

  • @elilivingston3802
    @elilivingston3802 Місяць тому

    explains it very well thank you soo much

  • @satyajeetarya7790
    @satyajeetarya7790 5 років тому

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

  • @kingarth0r
    @kingarth0r 7 років тому +6

    0 to the 0 is one because of this law

  • @Touch-me-not-Muni
    @Touch-me-not-Muni 5 років тому

    Gud understanding... Thnk u a lot sir

  • @user-zt8bv9ey1t
    @user-zt8bv9ey1t 11 місяців тому

    This is a lifesaver! Thank you!

  • @s.a.4397
    @s.a.4397 5 місяців тому

    Thank you! Awesome!!

  • @leigh181
    @leigh181 6 років тому

    Hey, can you let me know which program you use to record these vides. Do you write on an ipad and use screen capture technology?

  • @Rayce001
    @Rayce001 3 місяці тому

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