Binomial Expansion : Rational Powers : ExamSolutions

Binomial Expansion - Rational Powers.
See the Binomial Expansion Ultimate Revision Guide • Binomial Expansion
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[@mimillama]

I can see how the comments range from 9 years ago till now. This just shows how helpful these videos have been for almost as long as a decade now. Appreciate it man!

[@Skywalker-pd2qy]

Amazing ain't it..? Some professors just ramble on without explaining the core concept. I just love his videos, clear and precise

[@ridzwansaiful2735]

Absolutely agree

[@ExamSolutions_Maths]

A donation is always very much appreciated to help with my running costs. Go to any page on my website where there is a video and you will see a donate button. Thanks if you do.

[@junaidarshad2k]

You should add a reminder in the end to like the video! I always forget to do it... Anyways thanks for the excellent tutorials!

[@ExamSolutions_Maths]

Good point. Please like everyone.

[@ExamSolutions_Maths]

They will be infinite if the power is not a positive integer

[@alavi9494]

so the NcR formula can only be used when there's a positive integer power?

[@ExamSolutions_Maths]

+Alavi Steam That's correct

[@alavi9494]

+ExamSolutions thanks :)

[@nanaafiadwomoh8322]

What exactly is a positive integer power?

[@raindrop9314]

Nana Afia Dwomoh Acheampong if im not mistaken it is a any whole number >0

[@imperialrecker7111]

@@raindrop9314 well any natural number is only for NcR. other numbers like fractional, negative in the index would use this binomial expansion.

[@mariahalqubtiyah5269]

THANK YOU very very much. without you i'd be having a mental breakdown this exact moment.

[@helenday5031]

What a wonderfully clear explanation. And I'm so grateful the way this tutor frequently gives us guidance on the little (but hard!) things, those crucial links in the chain of understanding Maths generally and how it all works, that can make such a difference to how well we do..

[@suwalabhishek]

how long can these rational expansions go on?

[@ExamSolutions_Maths]

@naruto2710 The proof is beyond the scope of this level.

[@JacobKennedyowuor]

Very clear explanation there. thank you.

[@datboi1861]

Thanks so much for this. I was getting confused but you managed to clear it out. Thanks!

[@reaper7650]

Very nicely explained.. Great teaching..

[@MarcusOfficial1]

Thanks for all the help you give every young student. If there were a way you would like us to give back I will be welcome to try

[@danyold6494]

Thank you, I have watched basically all your videos.👍🏻

[@ExamSolutions_Maths]

That's a lot of hours!

[@danyold6494]

only papers though not the tutorials

[@ashwinirathi8343]

sir how we can expand more then two variable like(x1+x2+x3------)^n

[@avtaras]

Using polynomial expansion haha Which is pretty much impossible There is such a thing as "trinomial expansion" however it's ridiculously complicated. It is used in natural language processing.

[@angelikathakoor9646]

Thank you♥️ I had a hard time understanding this

[@TeamTTToxic]

Thanks, great examples

[@ExamSolutions_Maths]

You're welcome

[@SidG_huh]

Amazingly explained. Thank you so much!!! :)

[@danyold6494]

I will definitely donate

[@ExamSolutions_Maths]

Always appreciated

[@ExamSolutions_Maths]

@sbtccc You are perfectly correct. Thanks for that example.

[@SuprTorrent]

Is it possible to stop only after the first 2 terms, does it still correct, I've seen some they only take the first 2.

[@mwansachikonde4193]

Great video, what do i do when I'm told to Expand a similar binomial and also state the set of values of 𝑥 for which each expansion is valid. Anyone else can help me with this...

[@ansri24]

thanks bro

[@jonathanjones1186]

Thanks for uploading these videos, this has been really helpful for me

[@Cyno7]

is this the only method for binomial expansion. the formula just seems arbitrary to me. or do you have a video proving this formula.

[@moypatsiye9193]

I'm a bit confused as to how you cancelled all them 2s in the first example

[@CHARITYMUTIE-p4f]

Thanks so much

[@bobmudhina5108]

i really appreciate but i have a query on the workings of the second expansion

[@Aishathliusha]

your videos are very hepful.thanks so much.

[@Delta._]

Oh God finally! Finally! I can't express how happy i am right now. Can i pay you for thanks?

[@manalbani5447]

Thank youu!

[@miracle_of_india]

I am not clear that why do we have infinite terms for negative or rational index plz answer I have searched on internet but I did not get from anywhere

[@ExamSolutions_Maths]

When you carry out the n(n-1)(n-2).... calculation and similar ones. If n is an integer then at some point one of the brackets will be zero bringing the series to an end. This does not happen when n is a fraction or negative number so the series is infinite.

[@584emad]

sir, fractional powers always have infinite expansion right? but integers no?

[@ExamSolutions_Maths]

Positive integer powers give finite expansions, anything else gives an infinite expansion.

[@therelated1536]

no

[@opokuevans7971]

Thank you Boss.

[@lemonsilled7156]

you expanded it incorrectly in the third term of the first exapnsion...

[@goon227]

How so

[@ChandanKumar-ch7fg]

very helpful video........ thanks

[@nikite_9289]

Could you please explain why you get x^2 over 4 at 10:45. I thought that according to bidmas you would first square x making it positive and then times it by -1 which would logically give out - x over 4. Great videos anyways especially for homeschooling during quarantine

[@ExamSolutions_Maths]

(-x)^2 is (-x)(-x) which is x^2 it is not -1 (x ) (x)

[@nikite_9289]

@@ExamSolutions_Maths It clearly shows -1(-x)^2 doesn't it. So wouldn't you square the x first giving you a positive x and then times it by negative one making it negative

[@ExamSolutions_Maths]

@@nikite_9289 There are two -1's before it. so it becomes positive.

[@l1wlf457]

really helpful ser

[@codex7299]

superb🎉

[@ExamSolutions_Maths]

thank you!

[@tsudee8740]

thanks sir

[@Raghunandan-nk7zp]

I just came to know that Peter dury has started to teach math

[@harsh0811]

You said that we expect it to positive but the x^3 term in negative..

[@SuperHassaan2011]

It isn't. (-1)(-2)(-3)(-0.5)^3/3! = 0.125 i.e positive

[@aparichitunknown8943]

upto which term we need to expand it?

[@Delta._]

Physics Students : Just first two ( Ignoring the higher order terms 😎) Maths Students: A lot 😢 Btw I am a physics Student.

[@physicsxpro5050]

Mai problem is how many term required

[@jsytac]

This is wrong You cannot cancel all denominator '2's just because there is one [numerator] '2' on the top. You can only cancel a single '2'. As such the x^2 term should simplify to (+ x^2 / 4) NOT (-x^2 / 2) Equally the x^3 term simplifies to (-x^3 / 8) not (-x^3 / 2)

[@robinamunir9188]

there was square of 2x over there so we can cancel 2 twos in demoninator

[@kieratsahota6835]

Do we get given that formula?

[@ExamSolutions_Maths]

Yes.

[@tayibasneyha8637]

Didn't we have a condition set that n is a positive integer then how does a fraction work?

[@ExamSolutions_Maths]

There are some cases where n is either negative or a fraction. This tutorial takes care of this case.

[@tayibasneyha8637]

@@ExamSolutions_Maths Why can't ncr be used in this case ?

[@ExamSolutions_Maths]

@tayibasneyha8637 ncr can still be used to determine the coefficients

[@tayibasneyha8637]

@@ExamSolutions_Maths but when we put the value of n as a negative or fraction in the Calc it says math error. So eventually like you said we have to use the binomial expansion with factorials

[@theanimationmaster724]

@@tayibasneyha8637 I love how you ask “Why can’t ncr be used?” the immediately answer your own question you fuckin spastic.

[@ultimatsurvivalguide]

Is this formula given to us in the edexcel c4 exam?

[@ExamSolutions_Maths]

+ultimatsurvivalguide Yes, see page 5 qualifications.pearson.com/content/dam/pdf/A%20Level/Mathematics/2013/Specification%20and%20sample%20assessments/N38210A-GCE-Mathematical-Formulae-Statistical-Tables.pdf

[@ultimatsurvivalguide]

Thank you for all of your help. hopefully I do well this time

[@hamedhilal7113]

awesome

[@youssefsammouh501]

You deserve everything

[@thomasleung8644]

I don't understand why those expressions can be expanded. isn't 3/(2-x) already the simplest form and has no need to be expanded?

[@latifmozammel6924]

if only math was this simple =(

[@thomasleung8644]

Latif Mozammel but why isn't it the case?

[@Tessadog1000]

Thomas Leung that's supposed to be the point, expanding is supposed to make it less simple. if they wanted simplest form, they'd ask for you to factorise

[@tn7mu336]

Why aren't you my teacher?!

[@hadibhatti8941]

Sir is the formula provided in the exam

[@ExamSolutions_Maths]

Yes

[@bharatshukla3401]

I am waiting this video in 2023.

[@aldrichibia8302]

What if it isn't 1?

[@ibrahimshafi2064]

Take the factor out

[@imperialrecker7111]

make it in the (1+x)^n form

[@albaraazain6818]

You are amaziiiiiiiiing!! ^-^

[@debbie9.161]

Got an exam in two hrs🙂

[@timwood70]

at 4.44 you say it comes out as negative, but its 1x-1x-1 which is positive?

[@SaifulIslam-sc7kv]

F*ck u 😀

[@annadaisykpikpi8167]

THANK YOU!!!!! :D

[@renlonzanida6223]

Gordon Ramsay doing maths....nani

[@MakoMavuwa]

2024?

[@timwood70]

my bad i see it now... :3

[@plannedmurder]

is this the only formula that can be used for c4 questions?

[@ExamSolutions_Maths]

tom jones Yes, if the power n is not a positive integer.

[@jasonsiddall9740]

Great video, this has really helped me out of a spot.

[@adittoraian]

thanks a lot

[@ExamSolutions_Maths]

Thanks for watching and any support you give. Best wishes.