Binomial theorem | Polynomial and rational functions | Algebra II | Khan Academy
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- Опубликовано: 15 окт 2024
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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!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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"Let's just work through a few just to realize how quickly they get painful."
How encouraging.
Atleast he wasn't lying
well he offered a solution
just keeping it real😭
Good luck w your math tests everyone, wishing you luck 🤘
Harrison Hub mine’s tomorrow 😫
Thanks!!! Good luck to u as well💛
Thanks
I got an A 🌟
ভর্তিযুদ্ধে তোমাদের প্রস্তুতিকে শাণিত করতে জয়কলি পরিবারের ধারাবাহিক shortcut video থাকছে বিভিন্ন অধ্যায় এর উপর।আমাদের ভিডিও দেখতে নিচের লিঙ্কে ক্লিক করুন । ruclips.net/video/CyWK3V2wCzQ/видео.html
Thanks
This guy has a great voice
You are absolutely right.
Lowkey, he is 3Blue1Brown
@@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 🌎 🆙
Waste voice
Agree 😅
I don't know why I'm paying for college when youtube educators are way better teachers than the professors at my university.
Where you from?
Lol, I have to learn this and I'm just in the 9th grade 😭
.
@@damijinadu4184 I'm 12
They take their time to explain things for us to understand unlike university lecturers
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
bruh what kind of 4 year old's have you been hanging with?
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.
Wait you learn this in high school too i am in 8th Grade in Germany and i rivised this 3times
I feel u
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.
I just did myself a discouraging slap to the brain. 0:49
Jecille Esguerra yah I did skull dissection too to give myself a lovely slap on the brain ;)
😂😂😂😂
Thank you, 3 minutes into the video and I understand more than what my teacher lectured for 30 minutes.
Y would ur teacher take 30 mins .....
true as heaven
@@danielcliffgonmei9050teacher probably had to deal with multiple disruptions. 🙄
“if we say n choose k we remember from combinatorics this would be equal to...” no sir actually we do not remember
Frr period
Combinatorics is literally just the usage of the formula of Combination.
this is like maths ASMR
ভর্তিযুদ্ধে তোমাদের প্রস্তুতিকে শাণিত করতে জয়কলি পরিবারের ধারাবাহিক shortcut video থাকছে বিভিন্ন অধ্যায় এর উপর।আমাদের ভিডিও দেখতে নিচের লিঙ্কে ক্লিক করুন । ruclips.net/video/CyWK3V2wCzQ/видео.html
Is illuminati a real thing?
Khan: Let me colour code this.
Colour Cote Not Code
@@zhenix4616 No it is color code.
@@zhenix4616 Lol, it is code. It is hilarious when people try to depict themselves as smart by correcting others but get it wrong themselves
@@zhenix4616 r/confidentlyincorrect
I have a test in 2 hrs, thanks!
Hope you did great :) I'm going to do an exam (this is included) in about 12.
@ i wonder what he is doing now?
So how's life ever since that math test LOL
It's been five years but student around the world are carrying forward your legacy of living on the edge
raymond lay remember this. You still alive?
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
I almost lost hope to understand this until I bumped into this video. Can't thank u enough❤
These videos are highly invaluable and are far more concise than most material that you can find online. Thank you for your work, Sal. :)
I was lost since the beginning
the first few minutes were fine then he went to actual binomial theorem part and now my brain hurts
Rev limits harsh
@Rev limits Wow that's harsh :(
@Random Autonomous Drone Pilot not cool
@Random Autonomous Drone Pilot lmao ig im dumb too then
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. :)
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......
👌
Thank you. Black background with colourful text is amazing.
Finally
I got it
I got it
Much appreciated sir
This is the best explained way of teaching this topic
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.
Khan: "This comes straight out of combinatorics"
Me: "Straight out of Compton"
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..
been 7 years but still helping many people by this video.
Thanks for helping me to understand the binomial theorem ,sir!!!
Can we just appreciate how he has to continue doing this math and switching colors at the same time
Thank you! This is so helpful, I understand things so much more easily ;0
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 .
Could've just used Pascal's Triangle but that works too
Not when you're raising a binomial to the power of 20 and you need to memorize the 21st level.
Hahaha yeah
You can do 20Cx on the calculator though
Not when you're not allowed to use a calculator
@@wellwhatcanisay4489 except your welcome~
lovely explaination with easy understandable english
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
Wow, my professor never even explained what n choose k meant. What would I do without khan academy!
Please sir can you give us like 30 questions and solutions so that we can practice? God bless you thanks
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."
great job you really saved me
The best teacher in the world. The pioneer of online education.
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!
This theorom is so complex! I can't believe people can remember it!
FYI: I'm an 11 yr old student studying Algebra II.
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
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.
I'm in the 10th grade, and I learned more in this video than I ever had in my school.
Amazingly helpful video. Thank you.
Your way of teaching is awesome
my lecture never had time to take me through but you made it look better that way
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.
Salman khan, you’re a hero for me and my 7th grade friends in algebra 2, we are gonna school these sophomores!!
I’m preparing for my first year in the university as a student of mechanical engineering and I found your channel❤️
what a nice trick is this. I don't forget this formula.. Thanks a lot sir for making such these type of tutorial
Thanks. This tutorial helped me a great deal.
ভর্তিযুদ্ধে তোমাদের প্রস্তুতিকে শাণিত করতে জয়কলি পরিবারের ধারাবাহিক shortcut video থাকছে বিভিন্ন অধ্যায় এর উপর।আমাদের ভিডিও দেখতে নিচের লিঙ্কে ক্লিক করুন । ruclips.net/video/CyWK3V2wCzQ/видео.html
this is so much better than the plain old and boring The Organic Chemistry Tutor channel
explains it very well thank you soo much
this is amazing! so helpful I was lost before but then I replayed it and it finally made sense just phenomenal
I LOVE YOU AND I WILL BLESS YOUR ENTIRE BLOODLINE
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.
the first 6 minutes of this video taught me more than what my teacher taught my class for weeks on end.
Is there any trinomial theorem
What is the application ur using to write it down
really well explained! i understood everything. Thanks a lot
BRO IS DOING LOT OF HARD WORK in changing colors
Thanks.. This video helps a lot for me especially when our teacher doesn't teach at all.
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?
I’m really poor at math, so this was a lil confusing to me, but I understood it with your great examples. It soo after seemed easy, and correct me if I’m wrong, but this kind of reminds me of the narrative, or resolving methods of limits.
Sorry, just slapping myself on the wrist. . . Don't mind me.
People who put a squared plus b squared and forget the 2ab disgust me
Who else is solving number theory books all by themselves and these wonderful teachers are life??
Yo broo
I regret why I didn't pay attention to this channel during my school days 🥺, this is true gem 💎
exactly what I needed to see, thanks. It was nice to see you take the time to explain every step.
For the first time in history I've understood well something in maths ...
its very useful to learn maths while improving your english
You're awesome bro. Keep up the good work!
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 !!!
Jesus how much did Sal smoke before making this video?
carl sagan: "Bruhhh"
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.
At what level or grade do u start to learn this?
I don't regret watching this video. 💯📹📹
Is K always gonna be 0? Like a constant?
Yes.since power can never be negative, 0 is a good starting point
The best teacher ever 👍🏻👍🏻
I learnt this now i need to flex on everyone, i like it easy to learn
Truly earned my respect
Hats off for this guy
You guys should make an IB series as well. I promise if you charge $1 dollar for the course it will make you as rich as Elon Musk!!
Can you tell me how to derive formula for (x+y)^(1/2) by using binomial theorem or any other means?
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!
What would you do if the problem was (a+b)^52? Would you still follow this process?
Yes, this is the most effective method, much better than Pascal's triangle for huge powers like 52
Oh my goodness i understand! Thank you!
very helpful. thank you
Tremendous, excellent explanation, thank you, very much. God bless you tremendously. Thanks
How would you find the coefficient of a term if you have constants in front of a and b? such as: (3a + 7b) ^20
same process. for example, if you wanted to find the 4th term it would be (20C3)(3a)^17(7b)^3
simplify that and you have the coefficient
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.
You just changed my life
Khan Akademy is The Best Channel On RUclips!
Thanks you so much bro this helps me a lots
What tool do you use to draw all this stuff?
🎯 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
This is a lifesaver! Thank you!
I'm currently in year 11 (Aus) in isolation, ngl this was great thank you muchly
plz tell me what if the power is not a whole number like 4 but a fraction like 1/2 then what will be the values k?
ITS CLEAR AND EASY TO UNDERSTAND
Nice explanation!
I m from india this video is very helpful
Please make a video on multinomial theorem.........
How can express my thanks... Thank you very much sir.........
God bless you