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

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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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Пікірлер: 648

  • @andresleonardocastro5466
    @andresleonardocastro54663 жыл бұрын

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

  • @lelouchlamperouge3014

    @lelouchlamperouge3014

    2 жыл бұрын

    Atleast he wasn't lying

  • @maximcerta1641

    @maximcerta1641

    Жыл бұрын

    well he offered a solution

  • @kaylingardner_

    @kaylingardner_

    Жыл бұрын

    just keeping it real😭

  • @harrison85
    @harrison855 жыл бұрын

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

  • @thisisfrogx6808

    @thisisfrogx6808

    5 жыл бұрын

    Harrison Hub mine’s tomorrow 😫

  • @samaaalbaik

    @samaaalbaik

    4 жыл бұрын

    Thanks!!! Good luck to u as well💛

  • @alvincua4142

    @alvincua4142

    4 жыл бұрын

    Thanks I got an A 🌟

  • @monighosh6639

    @monighosh6639

    4 жыл бұрын

    ভর্তিযুদ্ধে তোমাদের প্রস্তুতিকে শাণিত করতে জয়কলি পরিবারের ধারাবাহিক shortcut video থাকছে বিভিন্ন অধ্যায় এর উপর।আমাদের ভিডিও দেখতে নিচের লিঙ্কে ক্লিক করুন । kzread.info/dash/bejne/da2LrZWPYtqpqrQ.html

  • @joshuastory7265

    @joshuastory7265

    3 жыл бұрын

    Thanks

  • @ellispaulk878
    @ellispaulk8785 жыл бұрын

    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

    4 жыл бұрын

    Where you from?

  • @damijinadu4184

    @damijinadu4184

    4 жыл бұрын

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

  • @seanammielantonio6386

    @seanammielantonio6386

    4 жыл бұрын

    .

  • @mariomario-ih6mn

    @mariomario-ih6mn

    4 жыл бұрын

    @@damijinadu4184 I'm 12

  • @ikeokyere3133

    @ikeokyere3133

    4 жыл бұрын

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

  • @Bottle502
    @Bottle5027 жыл бұрын

    This guy has a great voice

  • @izmasafa9582

    @izmasafa9582

    4 жыл бұрын

    You are absolutely right.

  • @peterkim994

    @peterkim994

    3 жыл бұрын

    Lowkey, he is 3Blue1Brown

  • @oscarstill909

    @oscarstill909

    3 жыл бұрын

    @@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 жыл бұрын

    Waste voice

  • @abdullahjaved2832
    @abdullahjaved28324 жыл бұрын

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

  • @zhenix4616

    @zhenix4616

    2 жыл бұрын

    Colour Cote Not Code

  • @RabanyMedo

    @RabanyMedo

    2 жыл бұрын

    @@zhenix4616 No it is color code.

  • @Jasmineaq

    @Jasmineaq

    2 жыл бұрын

    @@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 жыл бұрын

    @@zhenix4616 r/confidentlyincorrect

  • @jaesguerra
    @jaesguerra6 жыл бұрын

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

  • @RimazAboelgasim

    @RimazAboelgasim

    6 жыл бұрын

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

  • @PallaviAcharya

    @PallaviAcharya

    5 жыл бұрын

    😂😂😂😂

  • @alexdashkoff8583
    @alexdashkoff85833 жыл бұрын

    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

    Жыл бұрын

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

  • @IntenseNoobFPS
    @IntenseNoobFPS7 жыл бұрын

    this is like maths ASMR

  • @monighosh6639

    @monighosh6639

    4 жыл бұрын

    ভর্তিযুদ্ধে তোমাদের প্রস্তুতিকে শাণিত করতে জয়কলি পরিবারের ধারাবাহিক shortcut video থাকছে বিভিন্ন অধ্যায় এর উপর।আমাদের ভিডিও দেখতে নিচের লিঙ্কে ক্লিক করুন । kzread.info/dash/bejne/da2LrZWPYtqpqrQ.html

  • @help7456
    @help74563 жыл бұрын

    “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

    3 ай бұрын

    Frr period

  • @thomasbekkering
    @thomasbekkering3 жыл бұрын

    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

    @zhenix4616

    2 жыл бұрын

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

  • @muhammadhasanshaikhyuyings244

    @muhammadhasanshaikhyuyings244

    Жыл бұрын

    I feel u

  • @existentialrap521
    @existentialrap521 Жыл бұрын

    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
    @randynguyen20206 жыл бұрын

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

  • @danielcliffgonmei9050

    @danielcliffgonmei9050

    3 жыл бұрын

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

  • @prashamjain3635

    @prashamjain3635

    2 жыл бұрын

    true as heaven

  • @nicolettakouris

    @nicolettakouris

    Жыл бұрын

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

  • @teentalex
    @teentalex8 жыл бұрын

    I was lost since the beginning

  • @reese-794

    @reese-794

    5 жыл бұрын

    ur not alone

  • @imbrand5040

    @imbrand5040

    4 жыл бұрын

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

  • @joshvir262

    @joshvir262

    4 жыл бұрын

    Rev limits harsh

  • @zuro181

    @zuro181

    4 жыл бұрын

    @Rev limits Wow that's harsh :(

  • @hco4203

    @hco4203

    4 жыл бұрын

    @Random Autonomous Drone Pilot not cool

  • @Slayer_Abbyss
    @Slayer_Abbyss3 жыл бұрын

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

  • @CrimsonShoryuken
    @CrimsonShoryuken9 жыл бұрын

    I have a test in 2 hrs, thanks!

  • @user-xx5nk1wv1e

    @user-xx5nk1wv1e

    9 жыл бұрын

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

  • @DeZiar

    @DeZiar

    5 жыл бұрын

    @ i wonder what he is doing now?

  • @jett6865

    @jett6865

    4 жыл бұрын

    So how's life ever since that math test LOL

  • @akarshsharma2870

    @akarshsharma2870

    4 жыл бұрын

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

  • @milam9667

    @milam9667

    4 жыл бұрын

    raymond lay remember this. You still alive?

  • @ianwalniuk9757
    @ianwalniuk97576 жыл бұрын

    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
    @wiv_pro2 жыл бұрын

    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
    @mrinalinighosh95738 жыл бұрын

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

  • @sigmabond1289
    @sigmabond12897 жыл бұрын

    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
    @jaredwaters42936 жыл бұрын

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

  • @qhansen123
    @qhansen1238 жыл бұрын

    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.

  • @user-jn3dn4ss2i
    @user-jn3dn4ss2i5 ай бұрын

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

  • @10ksubswithoutoriginalcont65
    @10ksubswithoutoriginalcont655 жыл бұрын

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

  • @eduardorodriguez-oj3zc
    @eduardorodriguez-oj3zc10 жыл бұрын

    Finally I got it I got it Much appreciated sir

  • @mercypeters7913
    @mercypeters79136 жыл бұрын

    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

  • @himalrana4177
    @himalrana41777 жыл бұрын

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

  • @syedaghaliaali3400
    @syedaghaliaali3400 Жыл бұрын

    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...... 👌

  • @kira1995
    @kira19953 жыл бұрын

    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.

  • @helloitsfire
    @helloitsfire3 жыл бұрын

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

  • @pixelblaze8284
    @pixelblaze82848 жыл бұрын

    great job you really saved me

  • @tylerdipietro4201
    @tylerdipietro42017 жыл бұрын

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

  • @ZigZagGod
    @ZigZagGod6 жыл бұрын

    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
    @streetbadger44633 жыл бұрын

    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 !!!

  • @Adam-qg8yt
    @Adam-qg8yt7 ай бұрын

    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

  • @Ou_dembele
    @Ou_dembele3 жыл бұрын

    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.

  • @zukisanimakapela9055
    @zukisanimakapela90559 жыл бұрын

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

  • @yashuppot3214
    @yashuppot32144 жыл бұрын

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

  • @cockerala1633
    @cockerala16335 жыл бұрын

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

  • @sanchezchris95
    @sanchezchris959 жыл бұрын

    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.

  • @medievalmusiclover
    @medievalmusiclover6 жыл бұрын

    You are a natural Professor! Thank You Sal.

  • @PrudentialViews
    @PrudentialViews Жыл бұрын

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

  • @Ibrahim-xq1wk
    @Ibrahim-xq1wk5 жыл бұрын

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

  • @axeskull5193
    @axeskull51937 жыл бұрын

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

  • @mobpod420

    @mobpod420

    7 жыл бұрын

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

  • @axeskull5193

    @axeskull5193

    7 жыл бұрын

    Hahaha yeah

  • @wellwhatcanisay4489

    @wellwhatcanisay4489

    6 жыл бұрын

    You can do 20Cx on the calculator though

  • @maricaloubser6733

    @maricaloubser6733

    6 жыл бұрын

    Not when you're not allowed to use a calculator

  • @imnotcrazyjustinsane9433

    @imnotcrazyjustinsane9433

    5 жыл бұрын

    @@wellwhatcanisay4489 except your welcome~

  • @raebanzuela5860
    @raebanzuela58606 жыл бұрын

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

  • @ShivaPrasad-hm5lk

    @ShivaPrasad-hm5lk

    3 жыл бұрын

    lmao means what bro😑

  • @abdallahkalthoum8255
    @abdallahkalthoum82559 жыл бұрын

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

  • @sandrasilva-uo1ui
    @sandrasilva-uo1ui4 жыл бұрын

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

  • @gcmr87
    @gcmr879 жыл бұрын

    Yes. This is amazing!

  • @iExplorer64
    @iExplorer646 жыл бұрын

    Thank you so much, this helped me a lot

  • @adityasaxena5651
    @adityasaxena56518 жыл бұрын

    really great explanation! Keep it up!

  • @smiley4634
    @smiley46342 жыл бұрын

    Truly earned my respect Hats off for this guy

  • 10 жыл бұрын

    Great explanation. Thank you so much.

  • @gadremiebeats7530
    @gadremiebeats75308 жыл бұрын

    Wow I finally understand this Thanks Alot

  • @om_unique
    @om_unique6 жыл бұрын

    Thank you. Black background with colourful text is amazing.

  • @vanithaas.krishnan9822
    @vanithaas.krishnan98227 жыл бұрын

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

  • @renewamulaudzi181
    @renewamulaudzi1814 жыл бұрын

    this was very helpful thank you!

  • @swetanjalisamal2792
    @swetanjalisamal27926 жыл бұрын

    Thank you so much. It was really helpful.

  • @mr.ontological9583
    @mr.ontological95839 жыл бұрын

    Jesus how much did Sal smoke before making this video?

  • @xxxexyz87

    @xxxexyz87

    9 жыл бұрын

    carl sagan: "Bruhhh"

  • @reddy_b_official
    @reddy_b_official25 күн бұрын

    This is the best explained way of teaching this topic

  • @prashamjain3635
    @prashamjain36352 жыл бұрын

    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 .

  • @maximcerta1641
    @maximcerta1641 Жыл бұрын

    really well explained! i understood everything. Thanks a lot

  • @ranveerjadhav928
    @ranveerjadhav928 Жыл бұрын

    lovely explaination with easy understandable english

  • @azeezaz7729
    @azeezaz77293 жыл бұрын

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

  • @s.a.4397
    @s.a.43975 ай бұрын

    Thank you! Awesome!!

  • @mariannemargarette9218
    @mariannemargarette92185 жыл бұрын

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

  • @hughjanus8450
    @hughjanus84502 жыл бұрын

    Very helpful, thank you!

  • @mac7858
    @mac78589 жыл бұрын

    Thanks. This tutorial helped me a great deal.

  • @monighosh6639

    @monighosh6639

    4 жыл бұрын

    ভর্তিযুদ্ধে তোমাদের প্রস্তুতিকে শাণিত করতে জয়কলি পরিবারের ধারাবাহিক shortcut video থাকছে বিভিন্ন অধ্যায় এর উপর।আমাদের ভিডিও দেখতে নিচের লিঙ্কে ক্লিক করুন । kzread.info/dash/bejne/da2LrZWPYtqpqrQ.html

  • @oureducationalhub2717
    @oureducationalhub27172 жыл бұрын

    Your way of teaching is awesome

  • @georgea.752
    @georgea.7527 жыл бұрын

    Excellent! Thank you very much.

  • @Aba9846
    @Aba98466 жыл бұрын

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

  • @zooiii7113
    @zooiii71137 ай бұрын

    Oh my goodness i understand! Thank you!

  • @sujonahamed556
    @sujonahamed5562 жыл бұрын

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

  • @harryk1126
    @harryk11265 жыл бұрын

    A blessing to mankind

  • @muhammadhasanshaikhyuyings244
    @muhammadhasanshaikhyuyings244 Жыл бұрын

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

  • @veer8243
    @veer8243 Жыл бұрын

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

  • @ruthmcevoy8300
    @ruthmcevoy83007 ай бұрын

    Amazingly helpful video. Thank you.

  • @LilCarl-pl6py
    @LilCarl-pl6py3 ай бұрын

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

  • @elilivingston3802
    @elilivingston3802Ай бұрын

    explains it very well thank you soo much

  • @kurtl.3773
    @kurtl.37736 жыл бұрын

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

  • @user-zt8bv9ey1t
    @user-zt8bv9ey1t11 ай бұрын

    This is a lifesaver! Thank you!

  • @lickidy_dickidy.4870
    @lickidy_dickidy.48704 жыл бұрын

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

  • @Touch-me-not-Muni
    @Touch-me-not-Muni5 жыл бұрын

    Gud understanding... Thnk u a lot sir

  • @georgeimmanuel4850
    @georgeimmanuel48503 жыл бұрын

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

  • @yvonne3745
    @yvonne37455 жыл бұрын

    Omg u saved my life and troubles. I thank you

  • @redpoka13
    @redpoka133 жыл бұрын

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

  • @Spinomaks
    @Spinomaks4 жыл бұрын

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

  • @alyashraf848

    @alyashraf848

    3 жыл бұрын

    Lol 😂😂

  • @scorpion2070
    @scorpion20703 жыл бұрын

    faleminderit

  • @jagannathnandy873
    @jagannathnandy8737 жыл бұрын

    ITS CLEAR AND EASY TO UNDERSTAND

  • @annieyang4763
    @annieyang47636 ай бұрын

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

  • @igasobczyk9600
    @igasobczyk96003 жыл бұрын

    very helpful. thank you

  • @aishusuresh1798
    @aishusuresh1798 Жыл бұрын

    man you teach so good

  • @GekiClaws
    @GekiClaws7 жыл бұрын

    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 жыл бұрын

    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

  • @submissivekoala
    @submissivekoala5 жыл бұрын

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

  • @cabdixakiimmuxamed4930
    @cabdixakiimmuxamed49308 жыл бұрын

    Thank you very much.i understand very well

  • @stevewest6133
    @stevewest61334 жыл бұрын

    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.

  • @satyajeetarya7790
    @satyajeetarya77905 жыл бұрын

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

  • @DennisBolanos

    @DennisBolanos

    4 жыл бұрын

    Solving our concept...

  • @sarwinr
    @sarwinr7 жыл бұрын

    thank you really help me

  • @SarveshKumar-ml5jd
    @SarveshKumar-ml5jd7 жыл бұрын

    THAT WAS VERY NICE EXPLANATION

  • @gm2407
    @gm24073 жыл бұрын

    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.

  • @bobbysepulveda9771
    @bobbysepulveda97712 жыл бұрын

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

  • @blackmotion8297
    @blackmotion82972 жыл бұрын

    Thanks you so much bro this helps me a lots