How to expand (a+b)^n (Binomial Theorem with a combinatoric approach)

How to expand (a+b)^n? Well, we can use the binomial theorem and let me show you how! This video also features Pascal's Triangle, a combinatoric argument, and how to find the coefficient of a term in an expansion. Coming up next, we will an Extreme Algebra part 2, the Generalized Binomial Theorem!

Binomial and trinomial theorem:
Bonus part: coming soon

0:00 (a+b)^2=a^2+b^2?
7:53 explaining the binomial coefficient
13:52 finding the coefficient of x^2y^3 in (2x+y)^5

[lonelybookworm]

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

[TheDslide]

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

[gnikola]

0:02 Newton was literally trembling and shaking

[therealAQ]

I almost had a stroke at the beginning D:

[fluffymassacre]

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

[gradecracker]

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

[arequina]

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

[Bloble]

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!

[jordantyler]

I thought it was April fools for a second

[GaryTugan]

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....

[sanelprtenjaca]

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

[hmmmm]

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. 🙏

[BabyXGlitz]

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.

[nadream_nadrm]

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

[pilifx]

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

[shuddhoshawttoroy]

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

[vasundarakrishnan]

0:12 look at him smiling at our confusion

[sebaseba]

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

[toqa]

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

[janernn]

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?