You explained a very daunting and seemingly complicated concept very simply. Thank you muchly. I am also experiencing the growing realisation that my maths teacher is shit.
to be honest if you're doing binomial expansions and you don't know what a positive integer is something has gone horribly wrong haha nice video though
I got A*s in gcse maths and additional maths, but I have a horrendous, unenthusiastic, and very dull teacher this year and I got a C in my AS mock, (some c1/c2 stuff), I have made huge improvements already just from your teaching (post-mock). Thanksyou so so so much, keep up the good work!
Your videos are amazing!!!!!! they have helped me soooo much during my Alevel maths, I would just like this opportunity to say a big thank you!! hope you continue making these vids and helping people :) much appreciated
It’s 2022 and this 13 years ago UA-cam video just saved me for my pure maths exam! I’m in 8grade and my sir has introduced this math chapter very last minute 😭but so so grateful to this channel!💜
i'm so grateful teachers like you exist, all my maths teacher does is telling students his life stories and stupid jokes, and instead of explaining things he gives you the answers.((((
I'm sitting an A levelmaths exam today and am slowly realising how bad of a student I've been the past 2 years... Thank you for helping me not face the consequences for my actions! :)
thank you so much. i don't learn well in the classroom at all, so i've had to try to find ways to teach myself. at the start of the year I was failing maths, now 2 days before the exam I actually feel like I understand it. this is the best way to revise and the best math videos on youtube i've found. thank yooooou!
@@robshah9347 I still failed maths! I taught myself Biology A Level and went to university, became a primary school teacher, left, now I'm doing an apprenticeship in Business Analysis.
You can use Pascal's triangle but the purpose of this tutorial was to demonstrate the combinations method. Pascals triangle method though is not so good for higher powers as it takes time to build up the triangle before you can start. It is a quick method for small powers though, that I agree with.
OMG it turned out 2 b so easy! Thank u soooo much I'm passin' C12 tomorrow and I finally understand this thing! I start lovin' maths with your tutorials:)
@faryalkk A question will tell you where to stop. Say, expand up to the term in x^3 or write down the first three terms. Something along those lines. Hope that helps.
i never understood this when my teacher was teaching me this......but after seeing your video i was like THIS IS EASY....u have my vote, keep making more videos :D
A great help - I sometimes confuse that say 2x to power zero = 1 because when we differentiate 2x to the power of 1 we get 1 x 2 and the zero becomes a 1 = 1x2 = 2. (I think I have got the two examples correct)
I have these for my homework at the moment. I cannot find where you show examples of how to do them if they have a minus instead of a plus. For example i have to do (4x-1)^4, do i just treat 'b' as '-1' or do i treat it as positive 1, but have a minus inbetween each part? Thanks
Is it okay to watch these videos if am doing the new spec for a levels my exam board is edexcel btw and my teacher isn't the best so was hoping if I could find a channel like this to learn all the content for a level maths. Apologies for the long question 😅
Yes it is. I generally cover all the topics now for the A-Level Pure Maths, Mechanics and Statistics. Further maths requires a few more video tutorials to complete though. Good luck
your website is great but sometimes i get frustrated and get lost on it , do you think you could put a annotation or link in description for the next video and previous video? thanks great tutorial
Update from last comment: A great help - I sometimes confuse that say 2x to power zero = 1 because when we differentiate 2x to the power of 1 we get 1 x 2 and the zero becomes 0 to power 1 = 1 so we are left with 1 x 2 = 2 and the x ".disappears." (I think I have done the two examples correctly)
@TheKrakatoa1 That wasn't the intention but a cool idea. These were early videos and the intro music if you can call it that became irritating to some and it was later dropped
Once you write out the first 3 terms and put in '...' are you mean to continue writing and figuring out the terms? Or will it specify in an exam question :|
I just don't really think it's as simple as teachers say it is. I mean, I totally understand it, but it's honestly about the same working as just expanding. Reason being is you don't just have to manually expand each bracket individually, let's take the example in the video, you could just work out (3+2x) squared, then just square it again, sure, it isn't something you can ALWAYS use, e.g if you have 2 fractions and both have powers, or if it's to the power of an odd number, but you could still just square your equation, and keep doing that until you can't do it anymore, then just write out what you got, then manually expand what you have left over. Long story short: These methods are actually practically the same length unless you either have multiple bracketed equations which both have powers, or if the powers are odd. Binomial expansion may be a LITTLE shorter, but in the long term it's not that much more effective, basically use binomial expansion if you're not great at expanding big numbers. (yeah that wasn't much shorter, was it, oh well, hope you get it anyway if you're reading this lol)
Also don't get me wrong, this video completely helped me understand binomial expansion, it was really helpful, but after understanding it I'm just not sure how much benefit there is to it.
I am very confused when you have to use this formula and when you have to use: 1 +nax + n(n-1)/2!.(ax)^2 + n(n-1)(n-2)/3!.(ax)^3 For example in q3 of c2 june 2008 you use the second formula but in q2 of c2 june 2009 you use the given here.. And they are both have positive integers.. Is it coming to do with it being (1 + ax)^n and not being (a + b)^n??
ExamSolutions really still be commenting/hearting comments 10 years later, talk about dedication.
You explained a very daunting and seemingly complicated concept very simply. Thank you muchly. I am also experiencing the growing realisation that my maths teacher is shit.
Yes indeed !
I my teacher is a beast, taught us this in ks4
@@aaronlad7697 I'm still in ks3 and I'm doing this haha
@@natalia63532 same
to be honest if you're doing binomial expansions and you don't know what a positive integer is something has gone horribly wrong haha
nice video though
😂😂😂or you ended up in the wrong class
Joey Awesomeness I feel attacked
A positive integer is a positive whole number, for anyone wondering lol
Literally I was thinking the same thing lmao
Got a maths test tomorrow, this really helped to remind me how to do it last minute, and it wasn’t boring aswell. Thanks!
You are the one youtuber i turn off my adblock for so you can profit
+SatanicFriedChicken Thank you
Same here :D
You are the reason i'm passing maths!!! Thank you a million times, all the way from South Africa! :)
How you doing
Thank you! :) Still helping students 12 years later...
I got A*s in gcse maths and additional maths, but I have a horrendous, unenthusiastic, and very dull teacher this year and I got a C in my AS mock, (some c1/c2 stuff), I have made huge improvements already just from your teaching (post-mock). Thanksyou so so so much, keep up the good work!
how you doing now, 11 years later? did you takw up maths at University or anything?
Your videos are amazing!!!!!! they have helped me soooo much during my Alevel maths, I would just like this opportunity to say a big thank you!! hope you continue making these vids and helping people :) much appreciated
Thanks. The intention is to keep making and improving the videos over time. Your support is appreciated.
Where the hell in calculator is the c button?
@@mr-bean2306 above the divide symbol
It’s 2022 and this 13 years ago UA-cam video just saved me for my pure maths exam! I’m in 8grade and my sir has introduced this math chapter very last minute 😭but so so grateful to this channel!💜
i'm so grateful teachers like you exist, all my maths teacher does is telling students his life stories and stupid jokes, and instead of explaining things he gives you the answers.((((
I think we are lucky in this day and age to have instant access to UA-cam when we need help with any kind of problem.
I'm sitting an A levelmaths exam today and am slowly realising how bad of a student I've been the past 2 years... Thank you for helping me not face the consequences for my actions! :)
thank you so much. i don't learn well in the classroom at all, so i've had to try to find ways to teach myself. at the start of the year I was failing maths, now 2 days before the exam I actually feel like I understand it. this is the best way to revise and the best math videos on youtube i've found. thank yooooou!
It’s been 12 years, curious to see how life panned out after Alevels😅?
@@robshah9347 I still failed maths! I taught myself Biology A Level and went to university, became a primary school teacher, left, now I'm doing an apprenticeship in Business Analysis.
write as [2+(x+2x^2)]^4 and use the binomial expansion (a+b)^n where a=2, b=(x+2x^2) and n=4
You can use Pascal's triangle but the purpose of this tutorial was to demonstrate the combinations method. Pascals triangle method though is not so good for higher powers as it takes time to build up the triangle before you can start. It is a quick method for small powers though, that I agree with.
thank you man straight to the point, just how i like it
Hes added music to the intro!
Ok
Have my As Maths paper tomorrow, didnt know shit about binomial before this while all my mates said binomial is free marks. Love this video so much
OMG it turned out 2 b so easy! Thank u soooo much I'm passin' C12 tomorrow and I finally understand this thing! I start lovin' maths with your tutorials:)
Good luck. Hope it goes well for you.
Is that a good or a bad thing?
Thank you so much honestly I learn more from you than i do from my ALevel Maths Teacher who I have lessons with 5 hours a week!
@faryalkk A question will tell you where to stop. Say, expand up to the term in x^3 or write down the first three terms. Something along those lines. Hope that helps.
i never understood this when my teacher was teaching me this......but after seeing your video i was like THIS IS EASY....u have my vote, keep making more videos :D
You made this super easy to understand!! My lecturer took 30 minutes to explain it and seemed super confusing, this is so clear! Thank you!
@MicNarcolepsy It is an identical sign. You should use it over an equals sign when you are not solving an equation.
Thank you so much for this video! I have a trig final tomorrow and this really helped out
Thank you so much, this was far better and far simply explained than my teachers did, they really overcomplicated it!
@pureexpose It's up to you but nCr for larger powers of n is quicker and easier. I use nCr all the time though.
Thank you so much!
I have been stuck on this for weeks and with my C2 exam coming up; can't thank you enough!
Wow, you've done in 10 minutes what my maths teacher couldn't do in 3 weeks!!!!
THANK YOU
xxxxxxxxxx
@MrPadzo Good to hear that you are making improvements. Hope it continues that way.
A good idea but one that will take time to implement over 2000+ videos. May do this during the summer.
@LikeItDeep Thanks for your comments on this and other videos. I hope your revision is going well.
seriously, thank you so, so much. were it not for yr videos i'd have no chance at all with this.
3 months of confusing nonsense gone! thanks for the video! it helped alot
@Kekuya write as (1+5xx)^-4 then use the binomial expansion formula (See my tutorial on the website)
A great help - I sometimes confuse that say 2x to power zero = 1 because when we differentiate 2x to the power of 1 we get 1 x 2 and the zero becomes a 1 = 1x2 = 2. (I think I have got the two examples correct)
@hunnybear20 Good question. You use another version of the formula 1+nx+n(n-1)x^2/2! +...This is shown in a later tutorial.
You are the best. No other videos are able to explain maths to me as well as you.
Thanks for your support. Best wishes.
@simplyavarice94 Thank you for your support - hope you continue to find the rest of the site just as useful
I have these for my homework at the moment. I cannot find where you show examples of how to do them if they have a minus instead of a plus. For example i have to do (4x-1)^4, do i just treat 'b' as '-1' or do i treat it as positive 1, but have a minus inbetween each part? Thanks
I don't think there's any other simpler explanation for this
Thank you
Hi I've got my Additional mathematics exam in a week and I'm soooo glad I've watched this! Thank you! :-)
coping with A level maths has been so much easier thanks to your vids so much better than my useless teacher, im soo grateful!!!!
Bruh this helps so much, I didn't understand this at all and now I'm do :)
Would you please make a separate section for as maths videos?
Thankyou! I haven't understood this all year until now..
I don't think I would have got an A in maths without you. Thank You.
Thanks man, I use your videos quite frequently and they always bring me to a solution, it's like having a tutor. Thank you
Which one is it?
i thank you from with all my heart you have made life much easier for many people.
And again Thank You very much.
No. If you have a scientific calculator then you will generally see it as nCr
Ughhh thank you so much!!!
You made me understand something I thought was so complex for my test tomorrow :)
Go on to my website check out the syllabus you are on or if not just click on Pure maths and look under Binomial expansion.
Is it okay to watch these videos if am doing the new spec for a levels my exam board is edexcel btw and my teacher isn't the best so was hoping if I could find a channel like this to learn all the content for a level maths.
Apologies for the long question 😅
Yes it is. I generally cover all the topics now for the A-Level Pure Maths, Mechanics and Statistics. Further maths requires a few more video tutorials to complete though. Good luck
I love this,, thanks
Thank you for watching.
@therealjordiano It will specify the number of terms or power to go up to.
your website is great but sometimes i get frustrated and get lost on it , do you think you could put a annotation or link in description for the next video and previous video? thanks great tutorial
you guys know what you are doing great staff right there
Jonathan mutema It's one guy.
Update from last comment: A great help - I sometimes confuse that say 2x to power zero = 1 because when we differentiate 2x to the power of 1 we get 1 x 2 and the zero becomes 0 to power 1 = 1 so we are left with 1 x 2 = 2 and the x ".disappears." (I think I have done the two examples correctly)
It is a function called nCr seen on most scientific calculators. Check out the tutorials on my website for this.
This video has made my day! I was trying to figure this thing out for hours. Man, you r my saviour!
you sir, are a scholar and a gent.
Can you explain how you came up with that formula? i didn't really understand where it came from and how it works
Very late I know, but for others wondering it’s from Pascal’s triangle
thx so much I was so confused on this topic this helped a lot
Will do and thanks
@anaslashko Happy to do so. Thanks
got my C2 exam tomorrow and this has just saved me, thank you!
Thanks, pleased to be able to help.
thanks a lot i now understand it
Wow thank you so much
No probs. Pleased to be of service.
Are we given the ncr formula in the exam ?
Thanks for the video
@Y5FK Yes: It's in the Edexcel formulae book
Thank you very much, your video simplified the concept
@TheKrakatoa1 That wasn't the intention but a cool idea. These were early videos and the intro music if you can call it that became irritating to some and it was later dropped
Once you write out the first 3 terms and put in '...' are you mean to continue writing and figuring out the terms? Or will it specify in an exam question :|
cracking video with a blistering soundtrack
What is the tool you use to write that seamlessly on the screen like that?
Pleasure - Hope you find more of my vids helpful if you get stuck.
Not sure what you are doing to get that answer. 4C2 = 6, 6 times 9 = 54, 54 times 4 = 216.
Another happy customer here too. Thanks man
Will do
thanks for the video, it was very informative,
could i ask if we will be given the formula in the exam, or should i memorise it?
That's unfortunate but thanks. I hope you can continue to make progress from my videos.
dude u basically saved my life !
I just don't really think it's as simple as teachers say it is. I mean, I totally understand it, but it's honestly about the same working as just expanding.
Reason being is you don't just have to manually expand each bracket individually, let's take the example in the video, you could just work out (3+2x) squared, then just square it again, sure, it isn't something you can ALWAYS use, e.g if you have 2 fractions and both have powers, or if it's to the power of an odd number, but you could still just square your equation, and keep doing that until you can't do it anymore, then just write out what you got, then manually expand what you have left over.
Long story short: These methods are actually practically the same length unless you either have multiple bracketed equations which both have powers, or if the powers are odd. Binomial expansion may be a LITTLE shorter, but in the long term it's not that much more effective, basically use binomial expansion if you're not great at expanding big numbers.
(yeah that wasn't much shorter, was it, oh well, hope you get it anyway if you're reading this lol)
Also don't get me wrong, this video completely helped me understand binomial expansion, it was really helpful, but after understanding it I'm just not sure how much benefit there is to it.
this is called satisfaction.
Excellent .. sir...
Thank you so much...
Thanks you so much this really helped a lot✨✨✨
Cool. It feels good to have saved someone. All the best,
That's good and thanks.
Thank you sooooo much, i found this extremely useful :)
Thanks a lot, this video made it seem very simple!!
Abdillahi Iza Cheers
Thanks for helping us ❤❤❤❤
Should be below the video if you are watching this on my site.
@TheBigbangtoplove No probs. To have your support is enough.
Does it matter if the x is a or b?
No.
I am very confused when you have to use this formula and when you have to use: 1 +nax + n(n-1)/2!.(ax)^2 + n(n-1)(n-2)/3!.(ax)^3
For example in q3 of c2 june 2008 you use the second formula but in q2 of c2 june 2009 you use the given here.. And they are both have positive integers.. Is it coming to do with it being (1 + ax)^n and not being (a + b)^n??
THANK YOU SO MUCH. I was away and this has really helped me catch up