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

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  • เผยแพร่เมื่อ 10 ม.ค. 2025

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  • @andresleonardocastro5466
    @andresleonardocastro5466 3 ปีที่แล้ว +796

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

    • @lelouchlamperouge3014
      @lelouchlamperouge3014 2 ปีที่แล้ว +22

      Atleast he wasn't lying

    • @maximcerta1641
      @maximcerta1641 2 ปีที่แล้ว +12

      well he offered a solution

    • @kaylingardner_
      @kaylingardner_ 2 ปีที่แล้ว +10

      just keeping it real😭

    • @lukazade1
      @lukazade1 หลายเดือนก่อน

      subaru natsuki is real for this

  • @harrison85
    @harrison85 5 ปีที่แล้ว +932

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

    • @thisisfrogx6808
      @thisisfrogx6808 5 ปีที่แล้ว +8

      Harrison Hub mine’s tomorrow 😫

    • @samaaalbaik
      @samaaalbaik 5 ปีที่แล้ว +5

      Thanks!!! Good luck to u as well💛

    • @alvincua4142
      @alvincua4142 5 ปีที่แล้ว +4

      Thanks
      I got an A 🌟

    • @monighosh6639
      @monighosh6639 4 ปีที่แล้ว

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

    • @joshuastory7265
      @joshuastory7265 4 ปีที่แล้ว +1

      Thanks

  • @Bottle502
    @Bottle502 8 ปีที่แล้ว +481

    This guy has a great voice

    • @izmasafa9582
      @izmasafa9582 4 ปีที่แล้ว +11

      You are absolutely right.

    • @peterkim994
      @peterkim994 4 ปีที่แล้ว +4

      Lowkey, he is 3Blue1Brown

    • @oscarstill909
      @oscarstill909 3 ปีที่แล้ว +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 ปีที่แล้ว +1

      Waste voice

    • @FatimaZahra-zw8hh
      @FatimaZahra-zw8hh 3 หลายเดือนก่อน

      Agree 😅

  • @ellispaulk878
    @ellispaulk878 5 ปีที่แล้ว +1852

    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 ปีที่แล้ว +6

      Where you from?

    • @damijinadu4184
      @damijinadu4184 5 ปีที่แล้ว +92

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

    • @seanammielantonio6386
      @seanammielantonio6386 5 ปีที่แล้ว +2

      .

    • @mariomario-ih6mn
      @mariomario-ih6mn 5 ปีที่แล้ว +18

      @@damijinadu4184 I'm 12

    • @ikeokyere3133
      @ikeokyere3133 5 ปีที่แล้ว +25

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

  • @alexdashkoff8583
    @alexdashkoff8583 3 ปีที่แล้ว +128

    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 ปีที่แล้ว +22

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

  • @jaesguerra
    @jaesguerra 7 ปีที่แล้ว +332

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

    • @RimazAboelgasim
      @RimazAboelgasim 7 ปีที่แล้ว +31

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

    • @PallaviAcharya
      @PallaviAcharya 6 ปีที่แล้ว +3

      😂😂😂😂

  • @existentialrap521
    @existentialrap521 2 ปีที่แล้ว +21

    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 4 ปีที่แล้ว +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.

  • @randynguyen2020
    @randynguyen2020 6 ปีที่แล้ว +105

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

    • @danielcliffgonmei9050
      @danielcliffgonmei9050 4 ปีที่แล้ว +1

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

    • @prashamjain3635
      @prashamjain3635 3 ปีที่แล้ว +2

      true as heaven

    • @nicolettakouris
      @nicolettakouris ปีที่แล้ว +1

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

  • @abdullahjaved2832
    @abdullahjaved2832 5 ปีที่แล้ว +190

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

    • @zhenix4616
      @zhenix4616 3 ปีที่แล้ว

      Colour Cote Not Code

    • @RabanyMedo
      @RabanyMedo 3 ปีที่แล้ว +6

      @@zhenix4616 No it is color code.

    • @Jasmineaq
      @Jasmineaq 2 ปีที่แล้ว +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 ปีที่แล้ว +1

      @@zhenix4616 r/confidentlyincorrect

  • @IntenseNoobFPS
    @IntenseNoobFPS 7 ปีที่แล้ว +102

    this is like maths ASMR

    • @monighosh6639
      @monighosh6639 4 ปีที่แล้ว +2

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

  • @help7456
    @help7456 4 ปีที่แล้ว +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 9 หลายเดือนก่อน +1

      Frr period

    • @biscuit5359
      @biscuit5359 3 หลายเดือนก่อน +1

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

  • @CrimsonShoryuken
    @CrimsonShoryuken 10 ปีที่แล้ว +176

    I have a test in 2 hrs, thanks!

    • @user-xx5nk1wv1e
      @user-xx5nk1wv1e 9 ปีที่แล้ว +3

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

    • @viewing-p2s
      @viewing-p2s 5 ปีที่แล้ว +1

      @ i wonder what he is doing now?

    • @jett6865
      @jett6865 5 ปีที่แล้ว +6

      So how's life ever since that math test LOL

    • @akarshsharma2870
      @akarshsharma2870 4 ปีที่แล้ว +6

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

    • @milam9667
      @milam9667 4 ปีที่แล้ว

      raymond lay remember this. You still alive?

  • @Slayer_Abbyss
    @Slayer_Abbyss 3 ปีที่แล้ว +14

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

  • @Redmi10Asss
    @Redmi10Asss 10 หลายเดือนก่อน +2

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

  • @ianwalniuk9757
    @ianwalniuk9757 7 ปีที่แล้ว +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 ปีที่แล้ว +14

    Finally
    I got it
    I got it
    Much appreciated sir

  • @teentalex
    @teentalex 9 ปีที่แล้ว +189

    I was lost since the beginning

    • @imbrand5040
      @imbrand5040 5 ปีที่แล้ว +14

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

    • @joshvir262
      @joshvir262 5 ปีที่แล้ว +3

      Rev limits harsh

    • @zuro181
      @zuro181 5 ปีที่แล้ว +20

      @Rev limits Wow that's harsh :(

    • @hco4203
      @hco4203 4 ปีที่แล้ว +8

      @Random Autonomous Drone Pilot not cool

    • @lotheeu2087
      @lotheeu2087 4 ปีที่แล้ว

      @Random Autonomous Drone Pilot lmao ig im dumb too then

  • @wiv_pro
    @wiv_pro 2 ปีที่แล้ว +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 ปีที่แล้ว +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 2 หลายเดือนก่อน

      Hope after rethinking you made the right choice

    • @comradesalman7625
      @comradesalman7625 2 หลายเดือนก่อน

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

  • @sigmabond1289
    @sigmabond1289 7 ปีที่แล้ว +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 2 ปีที่แล้ว +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......
    👌

  • @om_unique
    @om_unique 7 ปีที่แล้ว +27

    Thank you. Black background with colourful text is amazing.

  • @himalrana4177
    @himalrana4177 8 ปีที่แล้ว +7

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

  • @qhansen123
    @qhansen123 8 ปีที่แล้ว +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.

  • @helloitsfire
    @helloitsfire 3 ปีที่แล้ว +3

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

  • @PrudentialViews
    @PrudentialViews 2 ปีที่แล้ว +2

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

  • @pixelblaze8284
    @pixelblaze8284 8 ปีที่แล้ว +10

    great job you really saved me

  • @prashamjain3635
    @prashamjain3635 3 ปีที่แล้ว +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 6 หลายเดือนก่อน +1

    This is the best explained way of teaching this topic

  • @TheDinobam
    @TheDinobam ปีที่แล้ว

    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

  • @erick4908
    @erick4908 5 ปีที่แล้ว +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."

  • @axeskull5193
    @axeskull5193 8 ปีที่แล้ว +39

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

    • @mobpod420
      @mobpod420 8 ปีที่แล้ว +56

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

    • @axeskull5193
      @axeskull5193 8 ปีที่แล้ว

      Hahaha yeah

    • @wellwhatcanisay4489
      @wellwhatcanisay4489 7 ปีที่แล้ว

      You can do 20Cx on the calculator though

    • @maricaloubser6733
      @maricaloubser6733 6 ปีที่แล้ว +9

      Not when you're not allowed to use a calculator

    • @imnotcrazyjustinsane9433
      @imnotcrazyjustinsane9433 6 ปีที่แล้ว +5

      @@wellwhatcanisay4489 except your welcome~

  • @zobayerabdullah27
    @zobayerabdullah27 10 วันที่ผ่านมา

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

  • @raebanzuela
    @raebanzuela 7 ปีที่แล้ว +3

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

  • @mrinalinighosh9573
    @mrinalinighosh9573 8 ปีที่แล้ว +3

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

  • @kira1995
    @kira1995 3 ปีที่แล้ว

    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.

  • @piusadas2220
    @piusadas2220 4 ปีที่แล้ว +2

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

  • @Ibrahim-xq1wk
    @Ibrahim-xq1wk 5 ปีที่แล้ว

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

  • @georgeimmanuel4850
    @georgeimmanuel4850 4 ปีที่แล้ว

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

  • @bobbysepulveda9771
    @bobbysepulveda9771 2 ปีที่แล้ว

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

  • @muhammadhasanshaikhyuyings244
    @muhammadhasanshaikhyuyings244 ปีที่แล้ว

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

  • @spikespiegel9371
    @spikespiegel9371 ปีที่แล้ว

    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!

  • @submissivekoala
    @submissivekoala 6 ปีที่แล้ว +2

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

  • @mac7858
    @mac7858 9 ปีที่แล้ว +6

    Thanks. This tutorial helped me a great deal.

    • @monighosh6639
      @monighosh6639 4 ปีที่แล้ว

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

  • @azeezaz7729
    @azeezaz7729 3 ปีที่แล้ว +1

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

  • @Ou_dembele
    @Ou_dembele 3 ปีที่แล้ว

    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.

  • @oureducationalhub2717
    @oureducationalhub2717 3 ปีที่แล้ว

    Your way of teaching is awesome

  • @eatwater3282
    @eatwater3282 3 หลายเดือนก่อน

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

  • @graceychia6805
    @graceychia6805 2 ปีที่แล้ว

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

  • @scar-kq3cl
    @scar-kq3cl ปีที่แล้ว

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

  • @Kurashiro1963
    @Kurashiro1963 ปีที่แล้ว

    The best teacher ever 👍🏻👍🏻

  • @streetbadger4463
    @streetbadger4463 3 ปีที่แล้ว

    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 !!!

  • @wango6603
    @wango6603 2 ปีที่แล้ว +1

    I LOVE YOU AND I WILL BLESS YOUR ENTIRE BLOODLINE

  • @lickidy_dickidy.4870
    @lickidy_dickidy.4870 4 ปีที่แล้ว +2

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

  • @jaredwaters4293
    @jaredwaters4293 7 ปีที่แล้ว +1

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

  • @aadityatripathi9284
    @aadityatripathi9284 3 หลายเดือนก่อน

    BRO IS DOING LOT OF HARD WORK in changing colors

  • @smiley4634
    @smiley4634 3 ปีที่แล้ว

    Truly earned my respect
    Hats off for this guy

  • @Aba9846
    @Aba9846 7 ปีที่แล้ว +3

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

  • @fllyziescwt
    @fllyziescwt 2 ปีที่แล้ว

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

  • @LilCarl-pl6py
    @LilCarl-pl6py 9 หลายเดือนก่อน

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

  • @veer8243
    @veer8243 ปีที่แล้ว

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

  • @gm2407
    @gm2407 3 ปีที่แล้ว

    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.

  • @GekiClaws
    @GekiClaws 8 ปีที่แล้ว +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 ปีที่แล้ว +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

  • @mxrgxrtt
    @mxrgxrtt 6 ปีที่แล้ว

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

  • @kurtl.3773
    @kurtl.3773 7 ปีที่แล้ว

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

  • @falahmshali6158
    @falahmshali6158 5 ปีที่แล้ว

    Khan Akademy is The Best Channel On TH-cam!

  • @ZigZagGod
    @ZigZagGod 6 ปีที่แล้ว

    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!

  • @roberthuff3122
    @roberthuff3122 11 หลายเดือนก่อน

    🎯 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

  • @zooiii7113
    @zooiii7113 ปีที่แล้ว

    Oh my goodness i understand! Thank you!

  • @Spinomaks
    @Spinomaks 5 ปีที่แล้ว +2

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

  • @mr.ontological9583
    @mr.ontological9583 10 ปีที่แล้ว +114

    Jesus how much did Sal smoke before making this video?

    • @xxxexyz87
      @xxxexyz87 9 ปีที่แล้ว +17

      carl sagan: "Bruhhh"

  • @krsureka6549
    @krsureka6549 4 ปีที่แล้ว

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

  • @Rayce001
    @Rayce001 8 หลายเดือนก่อน

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

  • @aishusuresh1798
    @aishusuresh1798 ปีที่แล้ว

    man you teach so good

  • @gadremiebeats7530
    @gadremiebeats7530 8 ปีที่แล้ว

    Wow
    I finally understand this
    Thanks Alot

  • @medievalmusiclover
    @medievalmusiclover 7 ปีที่แล้ว

    You are a natural Professor! Thank You Sal.

  • @uktuhilrechok4271
    @uktuhilrechok4271 7 ปีที่แล้ว

    its very useful to learn maths while improving your english

  • @amd.35
    @amd.35 11 วันที่ผ่านมา

    Matthew 19:26
    With God all things are possible

  • @elilivingston3802
    @elilivingston3802 6 หลายเดือนก่อน

    explains it very well thank you soo much

  • @rafirafchaines8316
    @rafirafchaines8316 3 ปีที่แล้ว

    This man just saved my life

  • @cockerala1633
    @cockerala1633 5 ปีที่แล้ว

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

  • @sujonahamed556
    @sujonahamed556 3 ปีที่แล้ว

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

  • @redpoka13
    @redpoka13 3 ปีที่แล้ว

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

  • @yashuppot3214
    @yashuppot3214 5 ปีที่แล้ว

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

  • @firepigsam1410
    @firepigsam1410 3 ปีที่แล้ว +1

    1:03 yep that's it im failing.

  • @ruthmcevoy8300
    @ruthmcevoy8300 ปีที่แล้ว

    Amazingly helpful video. Thank you.

  • @harryk1126
    @harryk1126 6 ปีที่แล้ว

    A blessing to mankind

  • @hindiurmilamaam5518
    @hindiurmilamaam5518 6 ปีที่แล้ว

    I m from india this video is very helpful

  • @XiaoMingXing
    @XiaoMingXing 8 ปีที่แล้ว +42

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

    • @jef_f8751
      @jef_f8751 5 ปีที่แล้ว +5

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

  • @ChloeMukibi
    @ChloeMukibi ปีที่แล้ว

    This is a lifesaver! Thank you!

  • @yvonne3745
    @yvonne3745 5 ปีที่แล้ว

    Omg u saved my life and troubles. I thank you

  • @itumelengramatlo1899
    @itumelengramatlo1899 4 ปีที่แล้ว +2

    The voice makes you pay attention attentivelyB-)

  • @TechAmbition
    @TechAmbition 8 หลายเดือนก่อน

    Maaaan This Explanation is 🔥

  • @sebastiankowalczyk5957
    @sebastiankowalczyk5957 6 ปีที่แล้ว

    This video saved my life

  • @tylerdipietro4201
    @tylerdipietro4201 7 ปีที่แล้ว

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

  • @sophiecoorey5099
    @sophiecoorey5099 2 ปีที่แล้ว

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

  • @jagannathnandy873
    @jagannathnandy873 7 ปีที่แล้ว

    ITS CLEAR AND EASY TO UNDERSTAND

  • @abdallahkalthoum8255
    @abdallahkalthoum8255 9 ปีที่แล้ว

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

  • @maximcerta1641
    @maximcerta1641 2 ปีที่แล้ว

    really well explained! i understood everything. Thanks a lot