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How to Use the Binomial Theorem (NancyPi)
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- Опубліковано 18 сер 2024
- 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
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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. ❤
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.
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.
yee 👍👍👍
This woman is literally saving my A level maths 🤣. Thanks btw
I need A level further maths :'(
0:57 when you blink during a maths class
VerindraGproductions hahaha lol 😂
i totally feel that way
Lol
😂😂 true
Lol
I'm not even studying this in school but want to support and love Nancy Pi!
royda5eleven I didn't know she had a last name
Nancy's last name is well-deserved for her excellent Private Investigator skills! 👣 🔍🕵️♀️
Max π 😂😂😂😂😂😂😂😂
same😂
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.
I’ve been watching different videos trying to understand this concept for over an hour. Your video is very clear and easy to grasp!
FINALLY something that makes sense! Thank you for taking the time to explain this properly!
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!
So awesome! "NancyPi" is back!!!!! & im ready to learn😉
In less than 10 minutes you got me to understand what my textbook got me fuming about for over 30. Thank you 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 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!
Hey ❤
Nancy, I'm so glad that I found your channel! I was afraid that the UA-cam 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.
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!
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 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.
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!
(And Thank you!)
Do you know what kind of board she is using ?!?!?!!?
@@user-vq7ui7iq4p glass
Watching this during a test on my second moniter during a statistics test. you're a lifesaver nancy
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!
the amount of old men in this comment section...boi i know you ain’t in no precalc class....
whats precalc?
here atleast in asia we are forced to do "amath" and i am honestly still confused about binomial even after one year lol
吳大帝
Chill, I'm only 20.
I TOLD YOU NOT TO TOUCH IT! ......that’s even weirder
velveteencherrytart I’m a math major though...
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.
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
The only teacher who looks good and teaches good
I am so impressed with your calculations. You are a genius, thank you so much for all your help. You are a life saver
Good to have you back on the net, Nancy!
This is one of the absolute best math videos on UA-cam.
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.
Mam You are BEAUTY with the BRAIN you cleared all my doubts.
Thank you :-)
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.
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
Please make more videos you are one of the few people who can explain math concepts very well.
I hope she gets back all her subscribers
Gay !!
Exactly, that's the spirit Hammad! It makes me really gay (as in happy) watching her subscriber count go up! 😎
O R what happened to her bff channel with 300 thousand subs?
what happened?
Hammad Qureshi no u
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.
Welcome back, Nancy!
Thanks for the new video. I was hoping you'd do a video on this. Thanks Nancy!
I'm experiencing a different kind of expansion..
Yay!! Thank you so much for coming back! Teach me Euler's method pleaseeeee!
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!!!!
00:00 the best maths teacher was made
It's not in my school syllabus but Calmness in her voice forced me to learn this ! .. 🤤
I'm really happy to see that your starting back up again! I'm looking forward to learning more from your new videos!
Many don't know this, but Binomial Expansion can be used to find roots of a number. Example; (a +b)at n=2 power is a formula for finding a square root of a number, and n=3 power is for cube root and so on.
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.
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.
@@steam2277 I definitely agree with that. She really makes the concepts easy to understand.
Missed you Nancy. Glad to see your back doing videos your help is awesome. Thanks
8:54 "Good times, good times..." 😂
I am very happy,that u r back😙😙😙u explain everything in such a way that anyone can understood in a min....😇. I really face a lot of problems without u.....😔😔😔
I'm happy to see you active! Best will towards you Nancy!
You're back! Thanks for your videos. Best regards!
I hope she will be back with all of her video to teach us maths
She teach really well
and here my professor was making this problem seem so difficult; and you manage to explain it better in 5mins!
Thanks for the help
OMG Nancy i found you.. finally. I was searching for your videos in Mathbff..... Thank you for this channel....
good to see that you are back all the best dear nancy
Girl, I love your videos! You save my life all the time
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 ~
"Good times, good times." This girl is hilarious.
Oh shit! The messiah of UA-cam Math has returned!
Hey Nancy, could you cover some statistic topics such as the probability tree? You would be helping myriads of students like me.
Kids : Nancy Pi
Men : Voice ASMR
Legends : Binomial Theorem
I can't find a single thing wrong with Nancy.
Truuu
OMGGG MY LOVE IS BACKK, I DONT NEED THIS BUT I NEED 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!
The polygon Mnemonic device may even help more..
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 UA-cam can explain so nicely like u
Great job! Used this as a review for my licensing exam....it’s a great source for those already familiar with the process.
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 find the pink text hard to read, but the lesson is very well done.
Yeah, pink doesn’t work very well on that background. I’m glad you said something about that. I thought it was just me.
I do feel a little smarter though.
Please don't use Pink very difficult to read
John Barden yeah really stressful
Thank you Nancy!! I'm glad you're back.
YOU DESERVE MORE VIEWS, THE CONTENT YOU CREATE IS AMAZING
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
Im really interested in how you create your videos!
wow .... what my teacher never did right thank you Im in love with the channel with this i can top the class thank you
ur such a good teacher
When she said "Hi Guys!", my heart melt instantly.. Oh well... Focus!!!
😅😅😅
nancy is back...
Nancy is back ................ she is the best.
Am I the only honest one watching her videos? Not only does she make math easy to understand, but she is so attractive that she makes it addictive as well. Even a person who hates math (like I do) can suddenly develop an interest in math.
finally! THAnks nancy glad you're back!!!!!
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
aryan parashar Yes. That's a good one.
Pascal couldn't have put it better himself - difficult subject put so intuitive - well done Nancy - picked up combination theory as a bonus
You really are an amazing teacher. I am trying to learn graphing logs, lns, and log(e), domains, etc. Every video you have teaches me better than any teacher so far, I would rather pay you for the college math class! I’m paying someone that I can’t understand and have to go online to find someone to teach me instead. I don’t see any newer videos of you, which I hope isn’t a sign. Do you have any videos on graphing logs?
3:34 I can see the desperation on her face to use pascal's triangle
Omg u always come thru right before I gotta test thankkkkk uuuu👏🏾💜
My math love idol is back a true genius. Now back to learning more about intergers.
After all these years, still nobody does math teaching better.
i wish you'd be my maths teacher. Thanks
Simp
@Delamo Tesfaye I get that feeling bruh
@@s.a.s3213 Aren't we all
Glad she's back
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 ;)
Straight up some of the best teaching I've ever seen. Thank you!
Nancy please do some videos on Laplace Transfornm..I'm in great trouble
Inside Devil aren't we all! 😂😂
Lapdance?
illuminati pyramid lol =)
Please keep this channel going! I'm testing through pre-calc (hopefully) and this is the last thing i had to study. thanks so much for helping to clarify this, the book i'm using is a jumbled mess of words. good luck!
thank you for coming back💞
I never spent much time studying this 1st time around. The pattern is so simple I just memorized it. In today's world, where 2 countries are divided by a common language, the deeper meanings are harder to grasp.
Nancy, thank you.
Honestly Speaking I Did Understand This Way Better Than School, Thanks To The Queen Nancy!!!
Nancy, you’ve been my math rock for the last year! Thank you
I could listen to you all day... so awesome!
Welcome back!
Nancy it'd be awesome to see some physics problems. Physics can be a beast even when we've had the appropriate math levels.
Blended Vitamins I hate optics
Nancy knows the best
Elegant exposition of the binomial theorem! Thank you Nancypi!
omg you are back . will have some good nights studying maths