How to Use the Binomial Theorem (NancyPi)
MIT grad shows how to do a binomial expansion with the Binomial Theorem and/or Pascal's Triangle. To skip ahead: 1) for HOW TO EXPAND a BINOMIAL raised to a power, like (x + 3)^5, skip to time 0:57; 2) for how to find the BINOMIAL COEFFICIENTS with the FACTORIAL/COMBINATION formula, skip to time 03:29; 3) to use PASCAL'S TRIANGLE to find binomial coefficients for expansion, skip to time 09:32; 4) for how to write the expansion for a SUBTRACTION/DIFFERENCE binomial raised to a power, skip to time 13:11 - Nancy formerly of mathbff explains the steps.
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1) HOW TO START A BINOMIAL EXPANSION: If your binomial is something like (x + 3) raised to a power like (x + 3)^5, you have two parts of your binomial: x and 3. You're going to take each of those and raise them to different powers in each term of the expansion. You can start your expansion just by writing these powers out.. For the FIRST PART of your binomial, x, it will start with a power of 5 (your power number) in the first term of the expansion (x^5), and then in each term after the power will go down by 1 (x^4, x^3, etc. all the way down to a zero power, x^0). Then you take the SECOND PART of the binomial, 3, and multiply each term by a power of 3. The 3 factor will start with a power of 0 in the first term, so 3^0, and then will increase by 1 power in each term after.
2) HOW TO FIND THE COEFFICIENTS (with the FACTORIAL or COMBINATION method): Then there's one more number to find, a number that gets multiplied in front of each term, or a binomial coefficient. There are two ways to find the coefficients (for the Pascal's Triangle way, see below). To find the coefficients using the factorial, combination ("n choose k") formula of n!/(k!(n-k)!, each term has a coefficient number you find using an n value equal to the power number, 5, and a k value that runs from 0 for the first term up through 5 for the last term. This number gets multiplied by the other factors in each term, and then simplify for your final expansion.
3) HOW TO FIND THE COEFFICIENTS (with PASCAL'S TRIANGLE): You can instead use Pascal's Triangle to find the binomial coefficients. Whichever row of Pascal's Triangle has your power number in it, as the second number, is the row that gives you all the coefficient numbers you'll need for your expansion. Each coefficient is multiplied with its term, and then you can simplify the expansion.
4) WHAT IF THE BINOMIAL HAS SUBTRACTION? It's very similar. It's easier to think of the subtracted term as "adding a negative number", and then all of the negative number (in parentheses) will be raised to the power in each term of the expansion. Note: if the binomial have something like 2x - y instead of x - y, make sure that all of (2x) is raised to each power.
Edited by Miriam Nielsen of zentouro: / zentouro
Пікірлер: 978
Thank you for taking what, on the surface, appears to be such an intimidating formula and teaching it in such a clear, calm and peaceful way. Leaving the anxiety behind helps one to concentrate on the procedure without unnecessary distraction. I watched your video twice, stopping it step by step to make sure I understood the concepts you were teaching and it all became so clear and simple. I believe I can now apply the binomial theorem without the use of a calculator or Pascals triangle and for me that is an achievement. Thank you again.
@autistitello
3 жыл бұрын
yee 👍👍👍
Hello Nancy, I’ve watched Khan academy, mathantics, and 10 other channels trying to learn math. You explain most thoroughly. All math teachers are more interested in going fast, you go slow and explain every step. I appreciate you. ❤
@jayrum7303
Жыл бұрын
I agree, what makes her superior is she flows like a dance (very abstract, I know), where Khan Academy is very sloppy and choppy. One is very easy to follow and build upon quickly and the other less so. The instructor on the Math and Science channel is also very effective like Nancy Pi, but his comes from smooth delivery and obvious passion for the subject:) Nancy seems to be put off by math like it's a problem that needs solved (which it is). Math and Science treats math like it's oxygen.
0:57 when you blink during a maths class
@wisdomcongeal2110
6 жыл бұрын
VerindraGproductions hahaha lol 😂
@deluxe1030
4 жыл бұрын
i totally feel that way
@zxcHoward
3 жыл бұрын
Lol
@shresho2817
3 жыл бұрын
😂😂 true
@electric_deer2007
3 жыл бұрын
Lol
This woman is literally saving my A level maths 🤣. Thanks btw
@moazamdurrani1265
2 жыл бұрын
I need A level further maths :'(
I’ve been watching different videos trying to understand this concept for over an hour. Your video is very clear and easy to grasp!
I'm not even studying this in school but want to support and love Nancy Pi!
@CarlyDayDay
7 жыл бұрын
royda5eleven I didn't know she had a last name
@Max-vn9bl
7 жыл бұрын
Nancy's last name is well-deserved for her excellent Private Investigator skills! 👣 🔍🕵️♀️
@sonyrulesbladZ
7 жыл бұрын
Max π 😂😂😂😂😂😂😂😂
@Fahed-Osama
6 жыл бұрын
same😂
@ishanbhardwaj1071
4 жыл бұрын
Simp
You are a great teacher. specially because you talk slowly and give the student time to process the information you present. Please do not change.
thank you so much for coming back Nancy! you saved me from failing so much! Couldn't be grateful more than this. Please, please keep doing more videos! I admire you so much!
FINALLY something that makes sense! Thank you for taking the time to explain this properly!
Thanks for the new video. I was hoping you'd do a video on this. Thanks Nancy!
So awesome! "NancyPi" is back!!!!! & im ready to learn😉
You're such a good teacher. You explain the problems and formulas in detail so students can fully understand the theorem. This really helped me, thank you!
@theycallmeprofessor399
Жыл бұрын
Hey ❤
Nancy, I have really enjoyed your videos, and hope that you will continue with them. The videos that you have presented thus far, regardless of NancyPi or Mathbff, have helped me proceed through Calculus III.
Awesome, nailed it again. I was struggling with a-b expansion and now I am not - thanks for all the effort and work you put into these videos they are a wonderful and amazing resource.
Nancy, I'm so glad that I found your channel! I was afraid that the KZread community lost you after you graduated. So it's a delight to have you back! I just subscribed. And I'm looking forward to lots of great material from you.
Missed you Nancy. Glad to see your back doing videos your help is awesome. Thanks
Yay!! Thank you so much for coming back! Teach me Euler's method pleaseeeee!
Good to have you back on the net, Nancy!
Nancy, you're the first thing in the morning on my PC despite so much of workload. Can't stop listening to you.
You're back! Thanks for your videos. Best regards!
I am so impressed with your calculations. You are a genius, thank you so much for all your help. You are a life saver
Welcome back, Nancy!
I'm happy to see you active! Best will towards you Nancy!
Nancy so glad you're back. Love your videos, the best on the web. You have the ability to make things clear, easier and less painful, even with Trig Integration. Can you make more for the hardest calc BC subjects ? Such as areas bounded in Polar Graphs, Vector calculation, Multiple Integrals. Thank you ~
I'm really happy to see that your starting back up again! I'm looking forward to learning more from your new videos!
I had success in a calculus class 2 years ago by watching mathbff. Now my upper division Econ uses derivatives and I forgot the calculus. It was great to go back and watch those videos again. Thanks Nancy for the tutor classes! You are a gem!
Please make more videos you are one of the few people who can explain math concepts very well.
u are a rolemodel for me in my programme, civil engineer and math/physics teacher! First semester now though, but looking at your vids really motivates me, and make me wanna be more like you, they way you teach. the way you teach will be the future of teaching!! DOPEST @NanciPi
good to see that you are back all the best dear nancy
Girl, I love your videos! You save my life all the time
Thank you for teaching!! And welcome back!! You really have taught me a lot!!
Thank you Nancy!! I'm glad you're back.
finally! THAnks nancy glad you're back!!!!!
Is this for real? You're back? Holy smoke. I know I've been missing your video's and I'm probably not alone with that sentiment. Not that we have stopped learning maths every bit time we get. But I used to enjoy and learn so much from your video's at work during lunchtime, it was relax and educational at the same time, and so very very clear! So happy you're making awesome video's again!
@mfatal
7 жыл бұрын
(And Thank you!)
@user-vq7ui7iq4p
5 жыл бұрын
Do you know what kind of board she is using ?!?!?!!?
@bijoythewimp2854
5 жыл бұрын
@@user-vq7ui7iq4p glass
i like people like you,those who can explain for students not for their selves,unlike like these professors and doctors at the universities and colleges they are very good in explaining for their selves...thanks i like and love you.God bless!
Great job! Used this as a review for my licensing exam....it’s a great source for those already familiar with the process.
Omg u always come thru right before I gotta test thankkkkk uuuu👏🏾💜
happy that ur back!can u do some lessons on definite integration stressing only on substitution part plss. it wud be really of great help
Watching this during a test on my second moniter during a statistics test. you're a lifesaver nancy
thank you for coming back💞
Hi Nancy, your binomial teaching was so good that I understand from 0% to 100%. Thank you for ur free service. Its good if u can select pastpapers eg Cambridge Alevel and stuff and do and show how to tackle questions and all. Btw happy to see u back. My sis got 93 for maths from just learning for u. My exams are near too. Will let u know the results. Thank u once again.
Could you eventually do videos on parametric and polar equations? There's not a whole lot of those on youtube and the majority of them are not super helpful. Your videos are ALWAYS helpful! These videos help my students a lot for extra assistance/reinforcement of the material :)
I’m in love... with your way teaching math :) Please please please cover everything you can from calculus and discrete mathematics too like this binomial theorem.. Nobody else in KZread can explain so nicely like u
Straight up some of the best teaching I've ever seen. Thank you!
Mam You are BEAUTY with the BRAIN you cleared all my doubts. Thank you :-)
OMG Yayy Nancy's back! Could you pleasee make a tutorial video of Trignometry identities? they really go above my head and the video of trig basics on mathbff reallyyyy helped me!
@rocstonie2834
2 жыл бұрын
The polygon Mnemonic device may even help more..
Nancy, you’ve been my math rock for the last year! Thank you
thank you for teaching like a normal person so many math teachers just expect us to know why this is that or that is this but you explain everything thank you so much
I miss her saying " It's okay, you don't have to like math but, you can like my page.". It was cute. Anyway, thanks for the helpful videos.
love u nancy!!
OMG Nancy i found you.. finally. I was searching for your videos in Mathbff..... Thank you for this channel....
It took me about an year to find this channel of yours. Happy that you are back!
Nancy, thank you.
8:54 "Good times, good times..." 😂
Glad you are back! I love your videos, you are the best.
Elegant exposition of the binomial theorem! Thank you Nancypi!
Yay I love Nancy!❤
I love you! thank you so much!!
Hey Nancy, you did a sneaky one! And there I was waiting for Mathbff to upload something. It's good to see you! :)
Hi, Nancy. Welcome back. Your videos are so helpful.
Hi nancy i realy love your videos. you made maths so easy and interesting i understand more from you than my maths teacher..its help me a lot.. pls do make videos on CONTINUITY
@CarlyDayDay
7 жыл бұрын
aryan parashar Yes. That's a good one.
Glad she's back
I could listen to you all day... so awesome!
Thank you so much love this is what our professor revise with us multiply the exponents first and Expand it.I am leaning new thing from your explanation today because i know I have to multiply the powers first. Nice explanation.
Welcome back!
i've been beating my head against a wall trying to understand the "N choose K" or "N choose i" part of this. The last 3 videos i watched skipped that part. Thank you for breaking that down.
Wow you made it seem so easy...this was great!!!!!Your teaching is amazing ❤❤
This is one of the absolute best math videos on KZread.
Hey Nancy, could you cover some statistic topics such as the probability tree? You would be helping myriads of students like me.
I hope she gets back all her subscribers
@hammadqureshi7351
7 жыл бұрын
Gay !!
@Max-vn9bl
7 жыл бұрын
Exactly, that's the spirit Hammad! It makes me really gay (as in happy) watching her subscriber count go up! 😎
@Santificated
7 жыл бұрын
O R what happened to her bff channel with 300 thousand subs?
@cheesywiz9443
7 жыл бұрын
what happened?
@12bymax
6 жыл бұрын
Hammad Qureshi no u
and here my professor was making this problem seem so difficult; and you manage to explain it better in 5mins! Thanks for the help
YOU DESERVE MORE VIEWS, THE CONTENT YOU CREATE IS AMAZING
I hope you can make a Discrete Math playlist. That would be really helpful and awesome. Thanks in advance, Nancy. You're awesome! Don't let anyone tell you otherwise.
@steam2277
7 ай бұрын
If she taught discrete math, I would think she might recieve a nobel peace prize. One of the best teachers I've come across on the internet.
@FallofDarkness55-Resurrected
6 ай бұрын
@@steam2277 I definitely agree with that. She really makes the concepts easy to understand.
It's not in my school syllabus but Calmness in her voice forced me to learn this ! .. 🤤
NANCY! Stumbled across this video and your channel! Missed ya on Mathbff. Great instructor! SUBED!
Glad you are back! Thanks!
Welcome back to KZread =)
Im really interested in how you create your videos!
Nancy, thank you for the job well done. You make everything seems simple out of those horrific equations
Nancy! Nancy! Nancy! You make me want to start school all over again just so I can watch your math videos LMAO. Great videos! You have talent, that's for sure ;)
nancyy ur back^^
Excellent explanation great video you're fantastic please teach me more maths
Thanks, really appreciate how you break down the problem!
Thank you so much!!!! queen of explaining math into sth fun and rewarding to do
Thank you ever so much Nancy,my grandson is about to take IGCSE maths and this has been a bane of our lives,thank you for simplifying so much.
OMGGG MY LOVE IS BACKK, I DONT NEED THIS BUT I NEED YOU
Nancy, soooooh glad to find this. Thank you!!!
dear nancy your energy is so cool, always brighten up my day. I'm still watching your videos, re-watching for the sake of: a. your energy, b. review some topics, c. always learn new things and make my math thinking less error-prone. Thanks for helping me build a solid algebra foundation, it has helped me learn everything I was failing to learn/understand. I'm now currently taking an engineering course and bc of you I have made enough preparations to catch up to like, everything (Differential and Integral Calculus). I don't know how to help in creating more math contents but how about connecting with ur viewers and do Math Q and As, math problems and techniques ig? IDK, hope this helps tho. Oh also, how about help viewers to understand about math more like to think mathematically. Example: Integrating math concepts (algebra) IRL, linear and quadratic equations I guess for starters? Not really sure, but this is just a recommendation. We're rooting for you dear Nancy.
I hope she will be back with all of her video to teach us maths She teach really well
Nancy please do some videos on Laplace Transfornm..I'm in great trouble
@annawilliams7568
7 жыл бұрын
Inside Devil aren't we all! 😂😂
@TheWorldsStage
4 жыл бұрын
Lapdance?
I was initially an arts history major but thanks to Nancy's good looks I switched to engineering because I just love and support you!!!!
A very nice explanation! Awesome! Her soothing voice helps a lot too :)
nancy is back...
NANCYYYYYY!!!!! omg!!!!!
Great video!!! Math is fun and this theorem is tricky and my math teachers for college algebra wanted pascal triangle but I learned from tutors the binomial theorem but I got stuck on the coefficients and variable notations this was a big help!! Thank you and math it up!!!
Thanks, NancyPi, you really help me in the areas I was logging behind in class...
Honestly Speaking I Did Understand This Way Better Than School, Thanks To The Queen Nancy!!!
NANCY
I'm loving these videos
you are just so good. i enjoyed your lectures starting from Log. OMG you are really special Nancy