Is the binomial formula... obvious? | Quick Math

Ok, maybe not "obvious", but it's nothing you should hesitate to apply.

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[WrathofMath]

"The binomial formula...it's not a bad formula." - Jon's glowing review of the binomial formula

[alkankondo]

What a unique way of deriving this formula!! I never thought of it in terms of n-length strings. It's a very combinatorial way of looking at it. It's always nice when you can prove/derive a formula in more than one way. Also, video editing is ON POINT, as always! 👍

[MuPrimeMath]

No contest, this is the best explanation!

[mrluchtverfrisser]

I think you summed up the problem in the first couple of seconds:

"We all know what comes next, just from memory"

For most people, these things need to be taught by memorization, rather than by understanding. The steps to reproduce (a+b)^2 = a^2 + 2ab + b^2 can feel daunting, and 'counterproductive' vs just remembering it. Think also of the quadraric formulat as a good example of this.

This is mostly what highschool maths is based on. Knowing the steps is not required for most people to know, and remembering the steps is not something people are familiar with, so the emphasize is on memorization. One cannot really blame the system for this.

A big part of studying maths is thinking differently about these concept, and realizing that it is often easer to remember the process that created the formula. Since the process is logicall, and follows simple rules (like the distrivutive property), you don't have to remember that much anymore. I hope this video has shown this for at least some people.

Keep it up!

[false]

This is so much more intuitive!!!! Thanks for this.

[MrMentholSlim]

a video i understand more then half of? thats the most mind blowing part of all of this.

[MuffinsAPlenty]

Very nice! This is (roughly) how I explained it to my students earlier this term in my elementary number theory class. Well, I gave them the chance to try to figure out a proof in groups - all wanting to use induction and running into a roadblock - and then I showed them a counting argument. I enjoyed that lesson :)

[mathwithjanine]

Awesome derivation! Thanks for sharing! :)

[rhealastname]

I've always loved combinatorics so much but never learned this method. This is gonna be helpful!

[MichaelRothwell]

Beautiful explanation of a fundamental result.

[dramwertz]

Nice, i came up with the same explanation when first stumbling above n choose k

[socrates]

That's an awesome way to look at the binomial

[mustafaa]

It looks like you’re flipping us off in the thumbnail

[gabitheancient]

that's so... obvious, that's so cool fr

[thereisnospoon]

Reflectioooon, omg! This channel just got even better

[CrittingOut]

wait this is literally so much more intuitive than what I learnt in lecture

[IvoMiniMylk]

Great content bro! keep up with the good work ^_^

[frozenmoon]

Well, its more obvious than the proof of Fermat's Last Theorem for example 😃

[dyer]

Wow i never understood this formula before today!!

[wimvanvlaenderen]

How do you make your videos? do you actually write on a mirror or glass or something? I just cant wrap my head around how you do it