The Binomial Expansion | ExamSolutions

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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Online Binomial Expansion Calculator
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[@ExamSolutions_Maths]

*Sorry everyone but at **1:04:07** the the x³ term, should it be (112/81)x³ instead of (112/27)x³*

[@varungandhi2576]

Its ok

[@varungandhi2576]

Your video are so helpful

[@aaronthompson1383]

no its not its 336/27

[@leonardocoiro4746]

Also, at 1:06:53 should the term in x^3 be 520/81 x^3 instead of 472/27 x^3 ?

[@sadnansami]

I bloody swear, without this channel, I'd be astray of math knowledge. Keep it up, man. We need more teachers like you.

[@rossbaglin5872]

Sadnan Sami Stuart Sidders is an absolute hero to generations of maths students

[@KumolalaSavesta]

I bloody swear too man

[@george._mav]

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

[@blackjack3519]

These videos are so helpful for mock revision, please do more! :D

[@jooddooj11]

This man needs a nobel prize

[@egnicknoob]

I agree

[@kaborenoah3455]

I'm with you

[@NormanWasHere452]

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.

[@paris293]

ive just been revising binomial expansions, this will come in handy 😁

[@karanjaruhiu1203]

Thank you for the incredible teaching, that deserves a like!

[@sarahchantry3637]

Honestly, people like you are doing wonders for social mobility. Thank you so much!

[@takeihuewi1348]

your work helps us students from across the globe- thanks from dubai! happy new year

[@honkynel]

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.

[@MyMathsAdventure]

Thank you for this series. Amazing content and will help me greatly 👍🏼

[@bobtheagent9087]

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

[@spacedog101]

ur not a teacher. UR A HERO!!!!!! THANK YOU SO MUCH!

[@robertandre8327]

Thanks so much I have learnt what had never been taught to me I wish you were my math teacher physically🙏🙏

[@my_virtual_learning_hub_]

You're a good teacher sir,keep the videos coming

[@jenniferwilson5379]

thank you so much for making this so easy to understand, my teacher made it so complicated

[@jimoduya1154]

We need teachers like you thanks you

[@seher2876]

on 16:05, i don't understand how you get that answer as i followed the exact steps on the first example onto this one, I got all of the steps correct however my answer was atleast 3 times greater, please tell me what I did wrong

[@ismailmuhammedabdulle3172]

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

[@ExamSolutions_Maths]

Thank you that would be much appreciated

[@Ahmed-vs1ui]

Thanks sir i am still an o level student but these things interest me and u made me understand

[@dilly2047]

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?

[@chendasinyangwe8679]

🎉😊sir you're the best,I really appreciate you for what you have done

[@paulmaggiar8274]

I spent hours on this video. Thank you!

[@kokoaung2914]

What a clear explanation? Thank you.

[@khalidbinabdullah3605]

Thank You very much for this video. Very helful

[@ExamSolutions_Maths]

Thank you for using it and your comment. Best wishes.

[@misbahismail6241]

This video was soo helpful appreciate your effort🙌🏻

[@hrperformance]

Top class teaching 👍🏽

[@ExamSolutions_Maths]

Top class learner!

[@SpaceXPeekedツ]

Amazing video thank you so much! :)

[@ElizabethSibanda-v6h]

Thank you so much this was so helpful

[@lucianagrimson4790]

Hats off to you! You're the best!

[@nazirnazir1099]

you are the best that video helped a lot thank you sir!!!

[@mxhsvn_b7866]

I LOVE YOU SO MUCH OMG THANKS MAN

[@EvaristoBanda-df9in]

You are powerful mr

[@nitikadesai7976]

Thank you, this video is as awesome and amazing as you are !super helpful 😊

[@ibbyh2763]

"Yeah but it covers all the topics, gives you practice questions" nice vid

[@Ilya_012]

We do not deserve you, you are the best❤

[@doseofpineapples1379]

thank you sir I found this very useful.

[@BoomShax123]

Thank you for this useful video

[@roonyq]

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.

[@VK-il9kv]

THIS IS BRILLAINT THANKS SOOOOOOOOOOOOOOOOOO MCUH DUDE

[@2271masoud]

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

[@ExamSolutions_Maths]

Thanks for pointing that out, my mistake even though I knew to do that. Just careless writing on my part.

[@seeyar3302]

thankyousoo much!!

[@mikhaelhalbar417]

You are fantastic!

[@Sharmeen-fw4fx]

great work ! really helpful

[@ExamSolutions_Maths]

Thanks for your support

[@simonbeavan1061]

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!

[@ExamSolutions_Maths]

Yes it was expanded but then I go on to simplify all terms. Standard procedure.

[@youyankagin]

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?

[@ExamSolutions_Maths]

Take a look at this. It may help kzbin.info/www/bejne/g6KymYlvZpZjr5I

[@micahma9666]

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!

[@bijjuu2]

Thank you so much.

[@afraimuangnory7195]

THANKS A LOT

[@user-ko4qo1vv4e]

Hello sir, at 1:04:09 for the x³ term, should it be (112/81)x³ instead of (112/27)x³ ? thankyou

[@ExamSolutions_Maths]

oops! You are correct

[@user-ko4qo1vv4e]

@@ExamSolutions_Maths ok thankyou sir :) these are very helpful.

[@kieran_ax_mal]

I've been staring at my calculator for 15 minutes about this one... ;P

[@itsbryan8449]

yup same here @@kieran_ax_mal

[@garylee6893]

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

[@leonidasgranjero8913]

You the most close thing to god. Period.

[@rezamahmud5416]

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

[@Jo-ow7rb]

Life saver omg

[@shobhashridhar3867]

thanks a lot

[@ExamSolutions_Maths]

You are most welcome

[@kaizenzn]

thank you very much

[@mazinnasralla2036]

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!

[@ExamSolutions_Maths]

Oops the the x³ term, should it be (112/81)x³ instead of (112/27)x³

[@只攻與防-j9y]

29:48 should it be (n1)(a*n-1b*1) without the plus sign

[@twistzzzz3879]

Who watch this during lockdown? :D

[@frostedbg142]

God bless you!

[@hbmat9460]

Wery wery good bto..thanks..which program do you use

[@VK-il9kv]

tyvm this is v useful

[@rezamahmud5416]

I think you got the coefficient for x^3 wrong in 1:04:07. The denominator should be 81 instead of 27

[@ExamSolutions_Maths]

Oops the the x³ term, should it be (112/81)x³ instead of (112/27)x³

[@Alex-qr6vp]

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

[@ExamSolutions_Maths]

As I explained in the following 2 minutes.

[@chumbucket3170]

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?

[@airblade8287]

still need an explanation? e.e its been 9 months lol

[@samv2907]

At 38:08, isn’t it twice the other way round? Seems like a contradiction to me

[@seher2876]

exactly what I was thinking

[@panashechifamba4116]

thank you

[@rasebshameer5807]

At 42:50 I don't understand why there is how (kx) has a power of 1

[@ExamSolutions_Maths]

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?

[@rasebshameer5807]

@@ExamSolutions_Maths What do you mean we look at the term in x first which bit is that ?

[@ExamSolutions_Maths]

@@rasebshameer5807 Did you understand the first example on this page?

[@nafinmahmudshek8090]

Is this helpful for olevel as giving the exams in 7 gcse 😢

[@alexpo.epignosis6553]

Thanks very much. But why is example 2 on minute 41:37 having 10C3 yet we are expanding to the X^6

[@sadmanzaid420]

(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!

[@husseinadan1776]

Watching in 2024 and indeed am grateful 🙏

[@VK-il9kv]

will the answer be different if u swithc the a and b terms around in the bracket

[@humayunrashid8351]

Could you do videos on the large data set please

[@calcpost3641]

Sir what exam board do you teach because i am doing edexcel for a level maths

[@hashamahmed4665]

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

[@euniceantwi5339]

Can we also write terms in descending order?

[@e.t._2509]

How to solve for (1+ax)^fractional power in descending powers instead of ascending powers?

[@MK-gd7qk]

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

[@qesserzuhrah3378]

I know this is a bit late but is this for a levels or gcse?

[@imtiaz2512]

qesser zuhrah gcse

[@ExamSolutions_Maths]

A-level

[@qesserzuhrah3378]

@@ExamSolutions_Maths oh ok thank you:)

[@qesserzuhrah3378]

@@imtiaz2512 its ok it a levels tho:)

[@mohameda5325]

Sats

[@MidnightStorm4990]

Have to put it on 2x speed....

[@panashechifamba4116]

40:54 isn't it that the coefficient is suppose to be negative

[@ExamSolutions_Maths]

No. (-2)^4 is 16. No negatives

[@Lewis-nb7pn]

If it were outside of the range what would make them invalid.

[@ExamSolutions_Maths]

Yes.

[@hadijaffri9856]

I need to ask a question? Will u reply?

[@sully555]

Edexcel a level p3 new syllabus specimen paper?

[@lybahwaqas6418]

Oscar deservingg

[@aishaabdoo7064]

What about CIE

[@ExamSolutions_Maths]

Section 1, 2 and 3 are on Paper 1, sections 4,5,6,7 and 8 on Paper 3

[@sarahrehman9257]

I love you

[@arafatqq2106]

44:47

[@star123_12]

at 1:00:17 how did you get root 1.04, if I sub in the 0.01 into the root 1+4x I get root 26 over 5 but like without a calculator how are you meant to get the 1.04 its too hard no?

[@frostedbg142]

Thank you so much

[@humanaccount2754]

thank you