(a+b)² = a²+b² That's enough KZread for today.

@blackpenredpen

5 жыл бұрын

Comment of the day!

@toqa002

5 жыл бұрын

😂😂😂😂😂

@somatia350

5 жыл бұрын

lol

@abtuly

5 жыл бұрын

lol mate

@MrCmon113

5 жыл бұрын

(1+0)^2 = 1 = 1^2 + 0^2 It's true.

(a+b)² = a²+b² I was questioning reality for a second XD

@btdpro752

5 жыл бұрын

Same

@neilgerace355

5 жыл бұрын

That's actually good science. Always question what everyone thinks reality is:)

@TheDslide

5 жыл бұрын

@@neilgerace355 agreed but it can drive u mad if u do it too much

@yrcmurthy8323

5 жыл бұрын

Accepts when a or b = 0

@keescanalfp5143

5 жыл бұрын

@@TheDslide, yes, you were rapid, a second could be long enough. reality exists, well can be said to exist, thanks to your recognising truth about it, and thanks to your recognising the lies too. as to what everyone thinks about it, some of us had as a first thought drawing a / through the = . great clickbait for math lovers.

0:02 Newton was literally trembling and shaking

@fanimeproductionst.v.3735

5 жыл бұрын

He literally shidded and farded himself

I almost had a stroke at the beginning D:

2ab: "Am I a joke to you?"

Breaking news: BlackpenRedpen loses all of its subscribers after saying that (a+b)^2=a^2+b^2.

@neilgerace355

5 жыл бұрын

They didn't try it for themselves first, so they haven't listened what bprp always says :)

@blackpenredpen

5 жыл бұрын

Fluffy Massacre hahahahaha

I love how you explain this in such a layman's term.

I thought it was April fools for a second

I LOVE how you take a break from calculus to appreciate the humble Algebra! You have truly opened my mind to appreciate algebra once again!!! Cannot thank you once again since I am a regular viewer. YOU NEVER DISAPPOINT!!!!!

I really like how you explain theorethical math to a huge variety of people and I think everyone can understand it and not only those who did it in school alread. I think it´s really nice to learn new things even if you don´t need it in most cases because we train our brains with this and your love for math makes it even better to understand and makes me happy aswell. Great job keep up the work!

@MathPhysicsEngineering

Жыл бұрын

For those who are intrested to see a rigorous proof of the theorem, with detailed explanation of every step check a video on my channel called: Calculus 1: The Binomial Expansion Formula Derivation and Proof it is a part of the calculus playlist that I'm recording

This video is so educative. Pascal's triangle, factoriels, sign for summation, combinatirics and powers in one video...

@blackpenredpen

5 жыл бұрын

Sanel Prtenjača yea, this had so much and I was so excited to record 3 parts all in one day!!

also the the sequence 1 2 1 is the number of vertices you span when travelling diagonally from a vertex to the opposite vertex in a square. as a matter of fact each row in pascal's triangle represents an n-dimensional cube, so 1+5+10+10+5+1 = 32 or 2^5 or the number of vertices of the 5-dimensional cube.

thank you for this. I am trying to stop just mugging formulas my teacher is feeding me and trying to understand how formula is found. You are one of the only videos explaining derivation in so much detail. 🙏

Haha! you got me....I was so stunned I actually PAUSED the video 2 seconds after you wrote (a+b)^2 = a^2+b^2.... wondering what the heck had happened. Also scrolled down expecting to see a plethora of haters in the comments! So, I was quite surprised at the comments, and realized that I needed to watch more of the video before being surprised :) I really dig your humor! And it's not even April Fools Day....

Very nice and healthy lecture, helped me to conquer my syllabus, which was looking very difficult in my study material. Thanks Sir.

That's really well explained! Thanks!

Oh wow. This brings back long forgotten memories of high school. Thank you for yet another incredibly entertaining video

@blackpenredpen

5 жыл бұрын

Thank you!!! I am glad to hear it!! : )

Pulled a switcheroo with that first bit. My complex roots were quaking right there.

Very Good explanation!!!!

Such an amazing video❤️❤️, please do more videos on combinatorics and discrete mathematics.

Here’s the deal... your video was helpful and fun. Subscribed!

Thank you Cant wait for the general formula

@blackpenredpen

5 жыл бұрын

Its in the description now. You can have n being -2

La mejor explicación que he escuchado

I got so confused why you were covering this since I learned it when I was in grade 11, but then I remembered my highschool education was very weird compared to most places and isn't even taught that way here anymore.

helpful review, thank you :)

Thank you for good math video.

You are the best teacher

Thanks a lot!

0:22 oh I loved those Dr Peyam clips, I remember watching this :D

Amazing!

Thank you for sooo a great video :)

Finally a video I can understand and already know the solution of! Haha

(a+b)^2 DOES equal a^2 + b^2 though... ...in a commutative ring of characteristic 2

@MrCmon113

5 жыл бұрын

The only context that really matters.

@leadnitrate2194

4 жыл бұрын

Or if a or b=0?

@akshataggarwal4002

4 жыл бұрын

Or when a or b=0

Derivation of cycloid's area through integration next please .love the videos ,even if i cant understand some of them,cheers.

Woooow amazing

Hello...sir you are great... Love from india....

I learned more in the first minute than 5 yrs of high school

@darthsion3844

5 жыл бұрын

*FIVE years*

@sanatgoel3302

3 жыл бұрын

What country are you from

Very good Explanation BUD

MY HOMEWORK WAS ON THIS TODAY, YOU SAVED ME

Learning this rn in gr12 data management

Thanks mann

omg! this was very useful; thanks a lot; 🤸🙌🧘💕💕

I remember me learning that in high school!

Thanks

this blew me away

I like this Insert: good lighting

0:20 thank you so much I almost had a heart attack

You are amazing

Sir,can u give an explanation about why volume formula can use disk method ,but surface area we cannot use cylinder to approximate instead of frustum since it is infinite cylinder

Hey, I was wondering if you could do a video on the cubic formula, or just a way in general to solve cubic equations. I've been confused about this and haven't been able to find any videos that are easy to understand. Thanks!

The illustration you show in the beginning is very helpful but it can be explained much easier by using mathematics of the vedic to illustrate

You need a completely different approach for fractional and negative powers. It's an infinite series where the answer is the sum. If you have (a+bx)^k, you need to convert it to the following (a^k)(1+(b/a)x)^k and then the nth term is (a^k)+(a^k)[ ((k)(k-1)(k-2).....(k-n)(x^n)) / n! ]

Fun fact : Pascal's triangle gives the powers of 11

@anusheelsolanki1

5 жыл бұрын

Only till the 4th row

@leadnitrate2194

4 жыл бұрын

@@anusheelsolanki1 no, it does for all rows. Consider 1 4 6 4 1.when we call it a power of 11, what we really mean is (1×10^4 + 4×10^3 + 6×10^2 + 4×10^1 + 1×10^0) is a power of 11. Now consider row 5. The number here is 1 5 10 10 5 1. If you do the same (convert it into decimal), it becomes (1×10^5 + 5×10^4 + 10×10^3+ 10*10^2 +5×10^1 + 1×10^0) which is 161051, which is a power of 11.

@nalat1suket4nk0

2 жыл бұрын

@@anusheelsolanki1 nope

@nalat1suket4nk0

2 жыл бұрын

Only if you take by decimal expansion, row 5, 1 5 10 10 5 1 1*100000+5*10000+10*1000+10*100+5*10+1*1=11^5 Explanaiton: so because each row can be expressed as binominal expansion, let a=10 and b=1 Then (a+b)^n=(10+1)^n=11^n

@nalat1suket4nk0

2 жыл бұрын

A lot of patterns appear in pascals triangle like the sun are powers of 2, the fibonnaci sequence appears in the sum of special diagonals, serpeinski's triangle with odd/even, some patterns that are close to serpeinski's triangle appear with multiples of other numbers, 3, 4, 5,... The (real) diagonales show the triangular(2D), tetrahedron (3D triangle), pentatope (4D triangle),... And pascals triangle can be written as combinatorics,... A lot of same patterns appear in higher dimensions of pascals triangle, pascal simplexes

OH MY GOODNESS WAIT...... I'M SUFFERING OF TRYING TO UNDERSTAND THIS THEORY AND YOU'RE...... JUST MUCH THANKS 😭😭😭❤❤❤❤❤❤❤❤❤ I LOVE YOU REALLY 😹😭❤💛💜🌻

TS 5:00...very important and oft missed point. You sir are really doing the lord's work here. One of the bwst maths channel out there on youtube.

Can you explain Laplas transfer? And thanks for you for all your videos.. Everyone watching you love learn and love you Thank you again 🖤

For those who are intrested to see a rigorous proof of the theorem, with detailed explanation of every step check a video on my channel called: Calculus 1: The Binomial Expansion Formula Derivation and Proof it is a part of the calculus playlist that I'm recording

@dragonlovesdiamond9512

19 күн бұрын

ARE YOU 3BLUE1BROWN???

Wow, I remember this. We can use this to derive the definition of the derivative using this formula for power rule.

@blackpenredpen

5 жыл бұрын

Justin Lee Yes. And we can also write e as a series.

0:20 good save i almost had a stroke

Can you make a video on the Laplace transfer?

I was a bit stressed out until he crossed out a²+b² Edit: @ 12:43, when you've written n! = n*(n-1)*...*3*2*1, strictly speaking it will only be correct for n >= 5 right?

@rastaarmando7058

5 жыл бұрын

n = 1,2,3....

@phobos3898

5 жыл бұрын

No not nessicarily, n just has to be greater then one. He just wrote that for the example, it can also be written as n!=n*(n-1)*...*1

@akshataggarwal4002

4 жыл бұрын

@@rastaarmando7058 u didn't understood the joke sir!

You should do a^n + b^n or a^n - b^n next

@blackpenredpen

5 жыл бұрын

Factor those?

@thenewguy7527

5 жыл бұрын

@@blackpenredpen yeah.

Hiii im kinda new to this channel you seem really awesome and I kinda understand your lessons. I was just wondering if you have videos or are you planning to make videos tutoring basic calculus. And if you do, do you have a playlist for it. I'm still a freshman trying to go for engineering course thank youuu

@blackpenredpen

5 жыл бұрын

Jayvee Flores hi Jayvee and welcome !! Please see my description for my website and other resources. Thanks and hope you enjoy my content here

@jayveeflores7757

5 жыл бұрын

@@blackpenredpen Thank youu! Keep making videos your content is very awesome I am looking forward for more of your videos. Best wishes

I love Pascal’s Triangle... 😁

We want more aboht this issue

Bprp-(a+b)²=a²+b² Me-Nani?

@akshataggarwal4002

4 жыл бұрын

Omae wa mou shindeiru?

(a+b)^2 = a^2 + b^2 was too uncomfortable to watch. I had to cover it until you erased it. Thank you for not torturing me too long.

Does the XXYYY same to YYYXX ? count them all or just choose 1 of them, or I mean that the position is necessary for this case?

Please:: A pyramid with a square base, 4 m on each side and four equilateral triangular faces, sits on the level bottom of a lake at a place where the lake is 10 m deep. Find the total force of the water on each of the triangular faces.

W0W... 🙌🏻👍🏻👍🏻🥰

(a+b)^2 = a^2 + b^2 in certain cases (for example some modular arithmetic structures, or in vector analysis when a and b are perpendicular)

@blackpenredpen

5 жыл бұрын

Matti Kauppinen mod 2

@MK-13337

5 жыл бұрын

@@blackpenredpen And I think (a+b)^2 = a^2 + b^2 if ab =0 mod n (so for example mod ab, or if a=xy then xb or yb does it. edit: one of our abstract algebra homework questions was about proving a similar result to this but I forget the details)

I am just interested: Is there any way to use the binomial theorem for n being just racional? Maybe with calculating factorial with gamma funktion? Well there are some more problems but I guess there are smarter people than me which could help me x)

Man you should do a video about polynomial theorem

@blackpenredpen

5 жыл бұрын

Quitzé Chávez Part 3 is about trinomial. And that pretty much it.

Answer this please. A pyramid with a square base, 4 m on each side and four equilateral triangular faces, sits on the level bottom of a lake at a place where the lake is 10 m deep. Find the total force of the water on each of the triangular faces.

0:00 I-I-Is that... the Overwatch theme ? *_W O O O O O W ! ! ! ! !_*

Can you solve İMO problems? Have you got any achivement from that?

I feel like I understand everything in your videos and then I look at my homework and cry

What about negative sign? Please explain.

So, when you have a certain number of x's and a certain number of y's (partitions of n of course) you have multiple ways of representing that only because there are multiple x's and y's not because the position of those x's and y's matters obviously. Combinations are literally just pairings of n elements into unique sets of size k hence n choose k. Although, in the case of the binomial theorem the size of the set is always n you simply choose k out of n elements to be different; x not y or the other way around.

@justabunga1

5 жыл бұрын

Yep, that's correct. Some people confuse this with permutations. Both permutations and combinations are different due to the ordering. If you're trying to find this on your calculator, the formula that he wrote in this video is denoted as nCr, which is n!/(r!(n-r)!). Permutation is denoted as nPr, which is n!/(n-r)!. n and r must positive integers. 0!=1 by definitely of the empty set.

Please help. A pyramid with a square base, 4 m on each side and four equilateral triangular faces, sits on the level bottom of a lake at a place where the lake is 10 m deep. Find the total force of the water on each of the triangular faces.

I need help. A pyramid with a square base, 4 m on each side and four equilateral triangular faces, sits on the level bottom of a lake at a place where the lake is 10 m deep. Find the total force of the water on each of the triangular faces.

Thanks for your great job! Could you please make video about Multinomial theorem (x1+x2+x3+x4+...+xm)^n. Thats would be wonderful, isn't it?

@ampleman602

Жыл бұрын

I'll try to tell the ans

@ampleman602

Жыл бұрын

Wait

0:12 look at him smiling at our confusion

Please what channel did you refer to in your last two posts? Was it Fresh Toadwalker?

@blackpenredpen

5 жыл бұрын

Filip Kochan no

Tem algum vídeo demonstrando a fórmula do polinomio de leibniz .

@blackpenbluepen do you take requests?

If n is not a positive whole number, it should still be possible to apply the theorem, we just have to 「ｄｏ ｍｏｒｅ ｗｏｒｋ」 (Limits flashbacks intensifies)

@blackpenredpen

5 жыл бұрын

Hahaha, nice one!!! And that's part 2 btw.

That's nice! I also have a video on Binomial Theorem.

With the music and the way you said this is very easy, I almost believed you...

@blackpenredpen

5 жыл бұрын

1willFALL : )))))

Please calcul the integral from 0 to π/2 of tan(x) 🙏

@alexwhite9550

5 жыл бұрын

Diverges

@justabunga1

5 жыл бұрын

The answer goes to infinity, so it diverges. You can try checking it on your graphing calculator as fnInt(tan(x),x,0,pi/2), but the answer will show up as error, tolerance not met, or whatever answer it says there.

can u explain 8.25-8.37 , i dont really quite understand what do u mean 4 go down then got 2 something....

Lmao, he included the sphere graphic from that triple integral video 😂

15:30 We will get there eventually!

Can i get explanation about integral, when we using subtitution integral and using partial integral, and maybe some example, i'm just confused how to use it xd

How u slove x^x=e?

Please let this be a new series.

@blackpenredpen

5 жыл бұрын

Nole Cuber Yes. We will totally get a “series” out of this Btw, part 2 is already in description

@papapapapapapageno

5 жыл бұрын

@@blackpenredpen pun intended;)?

Hello blackpenredpen. Why zero can't be used when applying binomial expansion to evaluate (1.01)4. I know this is easy when we express (1.01)⁴ as (1+ 0.01)⁴. Suppose we wish to express (1.01)⁴ as (0 + 1.01)⁴. Why this gives zero as a answer.

almost as good as 3

@blackpenredpen

5 жыл бұрын

Definitely!

What does your shirt mean?

Anyone know why Pascal's triangle spells out powers of 11 in every row?