Using binomial expansion to expand a binomial to the fourth degree

👉 Learn how to expand a binomial using binomial expansion. A binomial expression is an algebraic expression with two terms. When a binomial expression is raised to a positive integer exponent, we usually use the binomial expansion technique to easily expand the power.
The general formula for binomial expansion is given by (x + y)^n = summation from r = 0 to r = n of nCr (x)^(n-r) (y)^r. nCr gives the coefficient of the terms of the binomial expansion. The pascal triangle can be used in place of nCr to obtain the coefficient of the terms of the binomial expansion.
To expand a binomial, we continually add up the substitution of values into the general formula starting from when r = 0 to when r = n.
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Organized Videos:
✅ Sequences
• Sequences
✅Sequences | Learn About
• Sequences | Learn About
✅Determine The First Five Terms of The Arithmetic Sequence
• Determine The First Fi...
✅How to Write The Formula for a Arithmetic Sequence
• How to Write The Formu...
✅Find the nth Term of an Arithmetic Sequence
• Find the nth Term of a...
✅Find the First Five Terms of a Geometric Sequence
• Find the First Five Te...
✅How to Write The Formula for a Geometric Sequence
• How to Write The Formu...
✅Find the nth Term of a Geometric Sequence
• Find the nth Term of a...
✅How to Determine Arithmetic or Geometric Sequence
• How to Determine Arith...
✅Find the First Five Terms of a Sequence
• Find the First Five Te...
✅How to Write The Formula for a Sequence
• How to Write The Formu...
✅Find the nth Term of a Sequence
• Find the nth Term of a...
✅How to Simplify Factorials
• How to Simplify Factor...
✅Recursive Sequences
• Recursive Sequences
✅Prove the Sum by Induction
• Prove the Sum by Induc...
✅Find the Given Term of Binomial Expansion
• Find the Given Term of...
✅Binomial Expansion | Learn About
• Binomial Expansion | L...
✅How to Expand a Binomial
• How to Expand a Binomial
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👨‍👩‍👧‍👧 About Me: I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips. Find more here: www.freemathvi...
#sequences #brianmclogan

[@vishalbhatia6652]

Learn Vedic Maths my friend - you got stuck on -32*3 = - 96

[@brianmclogan]

thanks, happens to the best of us

[@vishalbhatia6652]

No worries. I teach Applied Vedic Maths

[@brianmclogan]

cheers!

[@aramish3037]

Pascals triangle is really hard to teach... he was just thinking about something else and couldn't multiply 32 x 3...

[@Dipp182]

Applied Vedic Math, that is just fancy talk for...You need 2 calculators and a Doctrine to know what I am talking about..

[@Illuym]

You actually just explained this better in a 6 min video then my professor did in my 3 hour lecture, thank you :)

[@esdan779]

Same

[@9b_b16_yatarjairolance2]

it's bcoz the way they communicate isn't concise and open

[@minty_macaron]

Wait…professor?! I’m deadass learning it in Grade 10..

[@celestinbelonie2099]

Had 20 mins to learn this

[@findingnemo92]

@@minty_macaron learning in 8th lol its hard af

[@mikecherri]

Every math instructor seems very passionate and fun, except for mine, absorbs the life out of the materials

[@hackdog1258]

Maybe you are the problem

[@kaiwilson5218]

I have to go online and watch math videos instead of my teacher's lectures because my teacher's voice is horrendous

[@ecebaris3841]

@@hackdog1258 how? It is a teacher's responsibility to make a subject more understanding and more fun for his students. There's no difficult subject. It's the teacher's fault, not the student's.

[@heuno8487]

@@ecebaris3841 but if the student doesnt put enough work what are they supposed to learn

[@almjrm5633]

You haven't seen mine he wants is to fail

[@corndig7395]

Only a Jr in highschool, I hated this lesson... this cleared up so much. Thank you

[@muhammadumar.9392]

I couldn't understand this topic in my university lecture.... but a million thanks to sir for making it this simple.... Huge respect for u

[@Lechatbleu-dd1wp]

Wow! 😶😀I really appreciate how enthusiastic you are. I REALLY WISH every math teacher could teach like that! Thank you SO much. You make me actually care about what I’m doing.

[@rb5587]

I love how this guy writes. Also thank you so much I would have done poorly on my test, but I learned this is 6 minutes instead of 10+ hours of worthless studying.

[@addyraper1291]

thank you so much for recording this, i honestly i would not have been able to understand it since i was attempting to teach myself how to do it because i've been out because of COVID, so thank you so much and i also love how interactive you are with your class!

[@brianmclogan]

You are very welcome!!

[@CristicMesper]

How same 😟

[@sinuhinjamescliefford2650]

Because of you ,I can answer now my recitation! thanks a lot

[@1mariomaniac]

He has a legendary expo markers lightsaber behind him that's how you know he's legit.

[@unstoppable-johns]

(2x+3)(2x+3) X (2x+3)(2x+3) If I expand and simplify the answer would be 16x4 - 96x3 + 216x2 - 216x + 81 If am wrong please correct me 🙏

[@kevinzhong23]

ty soooo much, this was so beneficial i cant lie at all. appreciate it.

[@vincentgo7633]

Sir what is your opinion.. Can I be an Engineer even though I'm not good in math?

[@brianmclogan]

yes, keep practicing!!!

[@patrickprah845]

Also in powers of even numbers your operation sign because , I learnt someone asked that (-3)^4 will be positive 81 because the exponent is even but (-3)^3 will be negative 27 because the exponent is an odd number 😊

[@ashleymahadeo5332]

His subscribers are either all his students or people like me who can't understand math over video calls in quarantine 😂

[@prowlandsasuke]

Me already crying because he didnt explain how he got those numbers for the triangle.

[@kats4ever608]

You add the two numbers above in the triangle and you start and end with 1

[@tehillahInc]

@@kats4ever608 imagine its power 23 it would be a tedious process. Do you have any remedy for that

[@pratyxx3169]

@@tehillahInc you can study combinations for that since it is the main factor behind those binomial expansions and that triangle is made to simplify combinations which can make calculations easy for short expressions

[@servant0017]

Thank you a lot, so far videos have just explained this to me through (a+b)^n and I need an actual problem

[@chelseapaytonlarry]

Omg, the exact question I was looking for! Wow that’s very convenient 😄

[@visiblygnomed177]

Thank you for making these videos. I hate this so much but these are helpful

[@brianmclogan]

Haha happy to help

[@hannahbanana9989]

i was literally having a break down cuz i couldnt understand this, I can now. tysm!!!!!!!

[@jnanasrija7915]

It is very clear. Thank you sir

[@brianmclogan]

you are very welcome!

[@lumineem4744]

I see people in the comments who are in college but I’m doing this in 7th grade and I’m very confused

[@cmace22]

Thank you for simply explaining what Khan Academy couldnt.

[@patrickprah845]

Please is this pascal or binomial theorem ? Because the description says binomial

[@anayahchowdhury7044]

how did u get 2x to the power of 3?

[@ridaakhtar9321]

ur doing gods work ma dude

[@deadshortgaming]

Thank you sir very long time iam trying to get the answer but I am not able to solve the problem but I understand and i will solve it

[@noura-561]

You’re really creative thanks👍💗

[@mrambo3218]

Thanks I was struggling to mulltiplyit out

[@brianmclogan]

You are very welcome!!

[@lassila3]

Struggled with this, understood the first time.....

[@razasyed575]

we love you brian mclogan

[@--076]

how do you come up with the numbers the triangle?

[@DianeRyanONeill]

Fantastic. Thank you!

[@ms.teacher2322]

Why are we using the plus sign?

[@brianmclogan]

don't like negative

[@francisaidoo5918]

Where is the -96 from

[@niko4617]

This guy is a life hack

[@Offical_Kelven]

Although the answers are close to correct... You provided little to know justification for why the calculations for the second to the last and the last term were calculated different... The sign could tell😢😅

[@carmenlopez7698]

Thank you so much this really helped!

[@RavindraSingh-cq5re]

Too good sir Where are you from sirr?

[@brianmclogan]

Florida, United States

[@RavindraSingh-cq5re]

You are wonderful

[@anayahchowdhury7044]

@@brianmclogan omg same!

[@LEO8C]

Just saved me 20 mins before my math quiz 😭😭

[@brianmclogan]

Boom

[@jrequintos9116]

whos still watching this 2021??? thanks the still helps

[@raynanwar2406]

i got so confused when i saw 481, and I got 81. I'm glad to see I didn't mess up.

[@user-ow6xm5zv8x]

How about (x+9)²

[@jessalabutap9396]

Sir, how do you get positive 216?

[@twangerrrrrr]

students and that one guy in the back made it mad awkward after saying 481

[@marriii3626]

This still does not make any sense

[@feje.benedict1146]

Very good

[@elliottrush2610]

Thank You you saved me my friend

[@patches393]

i got confused with the zero powers like -3^0 equal -1 so i got the first term negative

[@graciellaangelanebres8783]

Thank you for this very comprehensive video :) kudos!

[@itznia230]

This helped alot ❤

[@yngrid.playlist5297]

How about a multinomial with exponent?

[@hackdog1258]

Why is it always that the last term is y raise to the power of n

[@sea5205]

Thanks a lot!

[@AnnieUwUh]

You calm me down

[@princeofheroes7218]

I dont understand ant of this this is the first I heard of the binomial expansion theorem

[@tonmoybhuiyan2406]

Sir, i can't understand this It's Very confusing " I'm a very bad Student in math😥😥

[@zoel3096]

I miss real school so much i watch these to feel like im there

[@joshrose7890]

thank your mr. mathematical bald man

[@mahamettsedali9014]

Nice

[@envisdrako]

Thx

[@ToxikDnB544]

This guy looks like Nik Noisia

[@shunlu1217]

test on 28th, hopefully I can pass

[@scarlettbaltazar4121]

What if there was a y after the 3?

[@siyigou2990]

works the same..Just bracket like this (-3y) and add the power at the back

[@inyohmaryann8089]

There is something error in that explanation above negative and positive...

[@overwatchnoob8540]

All that work for one math question no way?

[@dylanwakefield7466]

I have an exam that I’m gonna fail tommorow on this, oh boy

[@zeyyyynep759]

İnsanların üniversite dersinde anlayamadıklarını söyleyince üzülüyorum türkiyede lise 2 de biz bu konuyu görüoruz ve üniversite sınavı için çok basit bir anlatım hedef ettiğiniz kitleye uygun ama türkiyede sınavlar çok ileri seviyede😢

[@Sosa_q]

I'm confused is this 8th grade math or college

[@Dipp182]

How do I apply this in the real world?

[@rohangreen8890]

Dip333 - To be honest, you don’t really apply anything past middle school math in real life

[@melanchinalmendral1364]

im confused in the 5th term, how did u get the 481? 😂

[@melanchinalmendral1364]

oh my bad,,, u fixed it

[@shashalom1347]

The ads is so funny.

[@SanthoshKumar-li4on]

What is binomial ? Sir

[@rohangreen8890]

Santhosh Kumar - A bit later, but an expression with two terms is known as a binomial.

[@rachit6586]

Koi Indian haen kya idher

[@destruc.5213]

Shit I Thought i was Johnny Sins

[@kasafieh265]

wow

[@saintanndecatur8926]

ur board is dirty

[@olliepubgmobile]

Cuz he writes on it!!!!!!

[@Dipp182]

Your*

[@officialbreddagav3426]

I am lost

[@demariuscoleman2149]

why so many dislikes

[@ENTJ616]

may I say your students doesn't respect you😅😅😅

[@shhhhank]

His eyebrows are too malicious

[@brianmclogan]

Haha yes

[@themcarrow3216]

Im failing. Is my teacher even supposed to be teaching this in sophomore year?

[@nickynickels4540]

TheMCArrow32 my guy I'm taking this freshman year and my teacher didn't even teach it. He gave it to us as a project over my break. Told us to make a lesson plan and basically teach it. Everyone got different topics about shit we don't even know

[@hard6338]

There should be a -81 a the last.

[@olianslow3943]

Md Mahir no its positive 81 because -3*-3 is 9, then 9*-3 is -27, then -27*-3 is positive 81.

[@brianmclogan]

thanks Oli

[@olianslow3943]

Brian McLogan welcome, thanks for the video

[@brianmclogan]

cheers!

[@parthpatel2712]

The 4th term is neg(136x) instead of 216

[@brianmclogan]

how are you getting that? 6*4*9 is 216

[@parthpatel2712]

Brian McLogan sorry sir ur right my mistake

[@samcowin7417]

This guy has no idea what he's talking about.

[@deimos7737]

Comment 100

[@AynRand1967]

A little dry

[@user-tb5nb9ez4w]

India teach better

[@ahzamarain6863]

Man's got slick handwriting but rly can't do simple multiplication😂

[@Legend-ts1pb]

Very poor math you have

[@VirusGod]

My Calc teacher, Mr Hunnicutt, would’ve explained this 6 minutes faster than you. Bahahahahahahahahaha Hahahahahaha bad calc teacher

[@ericsmith116]

What does this comment do for anyone? He was thorough, he slipped on a couple calculations but that happens to all math teachers every now and then. Why don't you teach a math class and we'll see how well you do with students and a camera on you.

[@wyomingcase7457]

Your intelligent comment shows us just how intelligent you are

[@rohangreen8890]

You have to remember that he is teaching a class and fielding questions as he goes. He is a fantastic teacher, I have learnt so much from him. So what if he stumbles a little bit? We all do.

[@nathanhab3591]

@@rohangreen8890 Exactly. Happens to the best of us.