The Binomial Expansion | ExamSolutions
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- Опубликовано: 9 сен 2024
- This is a complete revision guide for the Binomial Expansion
Section 1 : Introduction 0:00:55
Section 2 : The binomial expansion for a positive integral power 0:01:32
Pascal's Triangle 0:06:24
Example 0:07:18
Test yourself 0:10:16
Section 2.1 : Test yourself 0:13:24
Section 3 : The binomial expansion using nCr for the coefficients 0:27:28
nCr formula 0:19:50
nCr on a scientific calculator 0:22:54
binomial expansion formula with nCr coefficients 0:27:28
Section 3.1 : Test yourself 0:28:16
Section 4 : Finding specific terms and coefficients 0:31:34
Examples 0:31:45
Section 4.1 : Test yourself 0:38:52
Section 5 : Numerical approximations 0:44:40
Example 0:45:38
Section 5.1 : Test yourself 0:47:58
Section 6 : The binomial expansion for fractional and negative powers 0:50:57
Example 0:53:21
Section 6.1 : Test yourself 0:56:10
Section 6.2 : Test yourself 1:02:38
Section 7 : Validity (simultaneous type) 1:06:42
Section 8 : (b + a) to rational and negative powers 1:11:14
Test yourself 1:13:37
Section 8.1 : Test yourself 1:16:36
Section 9 : Partial fractions and the binomial expansion 1:19:51
Section 9.1 : Test yourself 1:24:06
Section 10 : Summary 1:29:24
------------------- Exam Questions ------------------------------------------------
Revision for sections 2 - 5
Edexcel Mixed exercise www.examsoluti...
Video solutions
Sections 2 and 3: Positive integer powers
Jan 2013 Q1: • Binomial Expansion : C...
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June 2012 Q1: • Binomial Expansion : C...
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Jan 2010 Q1: • A-Level Edexcel C2 Jan...
Section 4: Finding specific terms and coefficients
Jan 2011 Q5: • Combinations and the B...
Section 5: Numerical approximations
Jan 2012 Q3: qualifications...
video solution Q3a: • Binomial Expansion : C...
Section 6: Fractional and negative powers
Jan 2013: Q4: • Binomial Expansion : C...
Section 7: Partial fractions
June 2010 Q5: qualifications...
Video solution Q5a: • Partial Fractions : Ed...
Video solution Q5b: • Binomial Expansion : E...
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*Sorry everyone but at **1:04:07** the the x³ term, should it be (112/81)x³ instead of (112/27)x³*
Its ok
Your video are so helpful
no its not its 336/27
Also, at 1:06:53 should the term in x^3 be 520/81 x^3 instead of 472/27 x^3 ?
I bloody swear, without this channel, I'd be astray of math knowledge. Keep it up, man. We need more teachers like you.
Sadnan Sami Stuart Sidders is an absolute hero to generations of maths students
I bloody swear too man
This guy has literally saved me. Whenever i need to find a maths vid to help me understand a topic i come straight to this channel
These videos are so helpful for mock revision, please do more! :D
This man needs a nobel prize
I agree
I'm with you
Thank you for the incredible teaching, that deserves a like!
ive just been revising binomial expansions, this will come in handy 😁
Your website and all your content is phenomenal, thanks for providing this to us without asking of us in return. As someone who didn't do A-Level maths but needs it for uni physics your guides have taught me so much.
your work helps us students from across the globe- thanks from dubai! happy new year
Thank you for this series. Amazing content and will help me greatly 👍🏼
Honestly, people like you are doing wonders for social mobility. Thank you so much!
You're a good teacher sir,keep the videos coming
Great tutorial. I did this years ago but had forgotten it. This was explained very clearly and I felt like it brought it all back.
Pleas make more of these, its brilliant. No doubt I would of lost all marks if i had this type if question but now ill probs get all the marks. Will you do more of these?
ur not a teacher. UR A HERO!!!!!! THANK YOU SO MUCH!
Spent 15 minutes solving this 1:27:00 , then I realised I did it without the partial fractions yet surprisingly I go no calculation mistake. Thanks for the video
Thanks so much
I have learnt what had never been taught to me
I wish you were my math teacher physically🙏🙏
Thanks sir i am still an o level student but these things interest me and u made me understand
Thank You very much for this video. Very helful
Thank you for using it and your comment. Best wishes.
We need teachers like you thanks you
thank you so much for making this so easy to understand, my teacher made it so complicated
My only regret is that i did not find this channel sooner, nevertheless i make a pledge to spread its existence to Alevel students via any means necessary
Thank you that would be much appreciated
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I spent hours on this video. Thank you!
What a clear explanation? Thank you.
Oh my god. I am trying to get my head around this to help my daughter with her maths. I just about know what n means (any number?) and I can follow the overall logic, but what is C? Is that short for something? And is 'r' also any number?
Take a look at this. It may help ruclips.net/video/MqOhV9110y0/видео.html
Thank you so much this was so helpful
We do not deserve you, you are the best❤
Top class teaching 👍🏽
Top class learner!
Hey Mr. Solutions. Really loved this full revision guide. Is it just a series a of videos that you edited together or one that you made from scratch? Asking as I found it extremely helpful and wondering if the other topic playlists flow like this.
You are powerful mr
Hats off to you! You're the best!
Thank you, this video is as awesome and amazing as you are !super helpful 😊
I LOVE YOU SO MUCH OMG THANKS MAN
Very helpful!
thank you sir I found this very useful.
you are the best that video helped a lot thank you sir!!!
thankyousoo much!!
thank you so much for the timestamps
Thank you for this useful video
"Yeah but it covers all the topics, gives you practice questions" nice vid
THIS IS BRILLAINT THANKS SOOOOOOOOOOOOOOOOOO MCUH DUDE
THANKS A LOT
Thank you so much
thanks a lot
You are most welcome
Life saver omg
God bless you!
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Thank you so much.
Hello sir, at 1:04:09 for the x³ term, should it be (112/81)x³ instead of (112/27)x³ ?
thankyou
oops! You are correct
@@ExamSolutions_Maths ok thankyou sir :) these are very helpful.
I've been staring at my calculator for 15 minutes about this one... ;P
yup same here
@@kieran_ax_mal
Oh thank goodness! I have spent two days sending myself mad trying to find a solution that = 112/27 x^3 - I thought I'd lost the plot as I kept getting 112/81x^3 haha thank you :) - these are fabulous tutorials despite this slight error - moral of the story is to have some self confidence and to look at the comments sooner if you hit a problem lol many thanks G
I learn a lot from you. Thank you so much. I really like the calculator shown on your video. I like to get this calculator. Please give me the link to download this calculator. Thank you!
25:28 the second question mark is the coefficient of the second term of expansion and must be multiplied not added. it's a bit misleading for beginners
Thanks for pointing that out, my mistake even though I knew to do that. Just careless writing on my part.
how to solve this........in the expansion of (x² - a/x)7, the coefficient of x5 is -280 . find the value of constant a.................it is whole to the power 7 and x to the power 5
Excellent videos. I think there is an error in the x^3 term for the expansion of (4+x)(1-2x)^-1/3 at about 1 hour 3 mins but I am an hour in and enjoying maths!
Oops the the x³ term, should it be (112/81)x³ instead of (112/27)x³
tyvm this is v useful
great work ! really helpful
Thanks for your support
Is this helpful for olevel as giving the exams in 7 gcse 😢
Expanding the (2-3x)^6 bracket at 12:54 . Why do the answers have to be ^2, ^3, ^4 going up to 6 consecutively, wernt the values expanded from the previous line? Example 15(2)^4 x (-3x)^2 = +2160x, why has your answer been +2160x^2. Please assist. I massively appreciate your videos!
Yes it was expanded but then I go on to simplify all terms. Standard procedure.
At 38:08, isn’t it twice the other way round? Seems like a contradiction to me
You the most close thing to god. Period.
In 1:06:19 and also alike from previous example, how is modulus x less than half when x is written as less than half but greater than negative half? Probably I am not getting the concept of modulus right
Who watch this during lockdown? :D
Could you do videos on the large data set please
Can we also write terms in descending order?
How to solve for (1+ax)^fractional power in descending powers instead of ascending powers?
Wery wery good bto..thanks..which program do you use
will the answer be different if u swithc the a and b terms around in the bracket
Edexcel a level p3 new syllabus specimen paper?
29:48 should it be (n1)(a*n-1b*1) without the plus sign
Sir what exam board do you teach because i am doing edexcel for a level maths
Hi to anyone doing maths at as level- is binomial expansion with negative/fractional powers something i need to know does this come in my second year? Thank you
At 42:50 I don't understand why there is how (kx) has a power of 1
We want the coefficient of x so we look at the term in x first and x is the same as x to the power 1. Anything to the power 1 is always the same value. (- kx) to the power 1 is - kx. Does that help?
@@ExamSolutions_Maths What do you mean we look at the term in x first which bit is that ?
@@rasebshameer5807 Did you understand the first example on this page?
I think you got the coefficient for x^3 wrong in 1:04:07. The denominator should be 81 instead of 27
Oops the the x³ term, should it be (112/81)x³ instead of (112/27)x³
At 1:00:27, how would u know the surd form of the answer (when substituting 0.01) if ur using a calculator, how did u go about getting sqr 1.04
As I explained in the following 2 minutes.
Watching in 2024 and indeed am grateful 🙏
Hey Im abit confused on how my method got the right answer for the question at 38:36, I actually forgot to multiply the Ks by the powers of b. What I did was half 3840 to get 1920 and formed the equation: 1280k = 1920. which also gave me 1.5. Im unsure how Ive gotten the right answer, will this work only for this question?
still need an explanation? e.e its been 9 months lol
Thanks very much. But why is example 2 on minute 41:37 having 10C3 yet we are expanding to the X^6
(3+5x²)¹⁰ when 10C3 >> (10!/7!*3!) * (5x²)³ * (3)⁷
Notice 5x² is multiplied 3 times because 5x² * 5x² * 5x² ☰ (5x²)³
and then becomes 125x⁶ hope you understood!
If it were outside of the range what would make them invalid.
Yes.
I know this is a bit late but is this for a levels or gcse?
qesser zuhrah gcse
A-level
@@ExamSolutions_Maths oh ok thank you:)
@@imtiaz2512 its ok it a levels tho:)
Sats
What about CIE
Section 1, 2 and 3 are on Paper 1, sections 4,5,6,7 and 8 on Paper 3
Oscar deservingg
I need to ask a question? Will u reply?
40:54 isn't it that the coefficient is suppose to be negative
No. (-2)^4 is 16. No negatives
Have to put it on 2x speed....
I love you
44:47
thank you very much
thank you