Pascal's Triangle and the Binomial Coefficients

[AznBoiDaniel]

BE MY MATH TEACHER! You're so great at explaining things thoroughly and simply. You are very intelligent & the number one person i go to if i don't quite understand something in class haha. Thanks Patrick! :D

[Katherine7495]

your videos have helped me pass my IB Math class.. Thank you so much.

[patrickJMT]

@Katherine7495 glad i could help : )

[sexysoccerball]

this was so helpful i actually get my honors project now thank you sooo much

[UrbanAcer]

I had forgotten this from the holidays and I'm behind, Thanks so much!!!!

[patrickJMT]

@UrbanAcer no problem!

[Teagan126]

This was so helpful! Thank you'

[Joeweeeeeeee]

thanks

[TheCoolman5500]

you are great maaaan

in calculus 2 i will start from the beginning with you

thanks for everything

[AtsuikajiOtoko23]

I love you.

[VivaLaDivax]

I don't get the expantions.. how do you get those numbers and the powers?

can you please explain?

[VivaLaDivax]

Would this work as a math fair project?

A model, chart, and research?

please reply!

[ikillcat100]

thanks you are the best

[BrokePokemonTrainer]

what if its (a-b)? how do the signs between them end up? lets say.. to the 6th.

[emmiielii5]

@BrokePokemonTrainer it'll work the same way, however instead of having your b as a positive b, it'll be 6(a)^5(-b). If you have numbers to work with, just make sure you replace all the Bs in the equation with a negative number. When you add the two together, if its negative you'll be subtracting either way. :)

[MrMDarkmarker]

You've definitely made the right decision to post these videos judging from these amazing comments.

Thankyou so much for your a amazing help and guidence! You're a true hero.

[patrickJMT]

@MrMDarkmarker glad you like them. most people seem to as well, but you occasionally get a youtube troll lurking ; )

[mwanga1000]

this is great thnk you

[JackDanielsGirl89]

i love you.

[car1dona]

patricJMT you are the best thing that ever happened to me!! thanks for your help

[sagiterionmujtaba]

man U can really teach keep up the good work...!!

[BrotekkStudios]

O...M...G... You just explained in 5minutes what my teacher couldn't explain over three weeks. Thank you so much! Big exam tomorrow. :P

[patrickJMT]

@BrotekkStudios good luck! : )

[astrologio]

@patrickJMT Hey, you're a leftie. can't believe i didn't notice that earlier considering, i too, am a leftie. :}

Love your videos. Its true, some people just explain things better than others. I got to catch up with my failures in finite math. And watching your vids seem to do the trick. Thanks again. <3

[patrickJMT]

@BrotekkStudios point out that if you add up the number in a diagonal fashion, you get the fibonacci sequence (bonus points!)

[BrotekkStudios]

@patrickJMT Haha, I'm sure I'll be able to work that in there somewhere. :) Thanks again!

[marytiseli]

SUPER STAR you are! Merci Bien cherie !

[MrCrunchy29]

You explain things so clearly that a 2year old could understand. Good job mate!

[nikvenkata]

P-JAMM!



[7473302]

Im in the 7th grade n my mom tought me the long way n i got it N i showed her this video n She was like whoaaaa u could do that? xD

[plastig002]

fuck the mormans............

[diotus21]

i wonder why i was never taught this...

i feel neglected. TT-TT

[AnotherBrownKid]

is it just me or does the pink marker at the beginning look 3D?

[AZZAflipnote]

yeah i was sick for this part of the class, so i never really under stood it. thanks man.

[itouch286]

Hi, I have a problem. Could you please help me to solve it? A regular dodecagon with its diagonals.

a) How many line segments are on the diagram? Explain.

b) How many of these line segments are diagonals.

Thanks in advance.

[estreet1122]

pascals triangle is actually named tartaglias triangle but its just more properly known as pascals triangle

[007abhinavagarwal]

thank you so much

[dclaw294]

wow never heard of Pascal's Triangle....thanks now I can save some time!!!TG

[lexmarkx125533w]

Thank YOU !!!!!!......I learnt more on your youtube page than i did in my class...:D

[jayrox88]

Yoo make life soooooOOO much easier....ThanX for that ;)

[jayrox88]

you make life sooo much easier ;) than you for that Lol

[tennisgod12]

Saved my ass.

Thanks

[MrGhozt17]

we should plai xbox together sometime.

[Eba123456789]

youre my favorite teacher!

[jenniaqua]

Thanks so much! My teacher literally told us that our hw for the weekend was to study about Pascal's triangle and we would be quizzed about it on Monday. The text book told me NOTHING. So this really helped! :D

[Umashin]

thanks a lot that video really broke it down but what happens when the thing in the brackets have been divided a la (x+1/x) ^8. like i get the pascal part outside the bracket i'm just not 100percent on what to do with the 1/x in the brackets

[thezohan2112]

thankyou soooo much! i watched this vid and you explained it so clearly. 

[walshey1995]

patrickJMT i really have to thank you, this will be a big help with my maths assignment and take the stress off my brain. thanks again

[92010Jacabe2012]

Thank you Very much!

You explained Pascal's triangle very vividly

<3 math rocks <3

[ruveepon]

Show us something more challenging.

[LunaTicTacs]

Thank you. ^_^ I just thought I'd let you know that, thanks to you, unless I do really bad on the finals, I'll have the highest grade in my Algebra II class. (: Don't ever stop making videos! xD

[patrickJMT]

@LunaTicTacs ha, that is a nice feeling : ) congrats

[rshrott]

@patrickJMT you dont need to put the 1's infront of variables....its just cofusing

[patrickJMT]

@rshrott okie dok1e

[007abhinavagarwal]

Patrick is best

[yash9295]

do you know a site which shows tough pascal triangle problems?

[pinkprincessdl]

omg thank you dude! you are awesome! final exams tomorrow!

[buddhabunnee]

so much easier than the factorials.. thank you!

[twisted5abi]

thans man. really thanks 

[SomeHowSomeOne]

THANK YOU :D! you make it so much easier than my teacher! my teacher is always in a rush, and doesn't bother to put the n=0 beside the rows which really makes it looks so easy!

[MYSPACEISADISGRACE]

thanks so muchn for this vid. i have 4 days to write a 6 page reaseach on this and i thought i could teach myself by reading a book, but this is the 21st century so i just youtubed it :)

[kupkadaniel1]

thank you man, but you do not have a video about the convergence of taylor series :( would you make one please :)

[awesomesoccerfan]

I don't get it......why do people dislike this video?it is awesome.Thanks patrickJMT !!!

[Drsalimassal]

im so glad pople post these videos on here cause i cant understand jack from my virtual school classes without them

[SugaPete]

Great video! Thanks I really appreciate it, helped me with the derivative limit definition!

[Txtaholic4ever]

Oh my goodness thank you so much from a high school freshman! The way my teacher was teaching it, I was so lost. But this video helped so thanks a whole lot! I have a quiz tomorrow so i wont fail anymore thanks to you!

[patrickJMT]

@Txtaholic4ever good luck on the test : ) go TX!!

[UhMysteryGuest]

Better explanation than what my teacher taught me

[bcave500]

thanksss sooooo muchh im in all advance classes but the math is sooooo hard but the pyramid is ALOT easier than my teacher explained thanks aagain on behalf of a highschool freshman lol

[SuperMathmommy]

Seriously. If you don't know how to recognize that something is likely to be right or wrong your calculator can be a failure trap. One time just before a college Physics test, I was studying and I noticed that I was getting really strange answers on my calculator. I changed the battery and it was fine. But what if I didn't know the answer was strange? That is why we have to learn how to do things the hard way first. (Or at least one good reason.)

[patrickJMT]

@SuperMathmommy i found i made more mistakes with a calculator than without one.

[SuperMathmommy]

It may also be helpful to note that the second number in each row is the same as the exponent.

[sk8teh14]

@SuperMathmommy

that's essential to proving the basic derivative algorithm. (d/dx (x^n) = nx^(n-1))

[WillyLee23]

ALSO there is a pattern with the exponents in each term.

After the expansion, notice the first term starts at 1a^n for (a+b)^n.

Every term after the first, the exponents of 'a' decrease by 1 and the exponents of 'b' increase by 1.

[vanflymen]

Great video, thank you. It's easier to show that if you number each row from 0 to n, where the first row (the one that equals 1) is row 0.

You can easily write the coefficients, starting in the second row as (1C0)a + (1C1)b (where 1 is the row number and 0 is the item/column in the row).

So row 2 would look like this:

(2C0)a.a + (2C1)a.b + (2C2)b.b

row 3 would look like this:

(3C0)a^3 + (3C1)a^2b + (3C2)ab^2 + (3C3)b^3

etc.

Thank you for all your videos, they are awesome.

[TheTonylearner]

I think you did an awesome job. Clear and precise in your teaching. Thank you. Applause!

[aaronbau277]

thanks for the help...!!!

[SimPOrtia]

thnx alot, i av an exam tomorrow, can u make a video about logarithms

[patrickJMT]

@SimPOrtia did ya try looking to see if i had any videos about logarithms?

[sk8teh14]

Did you ever notice (keeping n representing the same variable) that 11^n follows the pattern of pascal's triangle (it breaks down at n=5 I think). 11^0 = 1, 11^1 = 11, 11^2 = 121, 11^3 = 1331, 11^4 = 14641

[sk8teh14]

lol, if anyone has a graphing calculator, they can just write a program with a loop and it'll do this in 2 seconds.

Your methods are ancient good sir, lol.

[SuperMathmommy]

@sk8teh14 I hope your batteries never die.

[sk8teh14]

@SuperMathmommy

alrighty then

[tikurgisila]

Bro, what if the sign is -?

[techking00107]

Thank you so much for this

[AusTanballa]

is there a way to get the coefficients on the calculator?

i have a homework problem that askes (x+y)^10 , n=4

so is there a way to solve that without drawing out 10 rows of the triangle?

[elsieascoli]

your video was a real  life saviour for me all the way in australia!~thanks a heap.

[akbar2k7]

Nice one great Vid I never realised Youtube coulc be a Acemedic reasource thanks. Gratitude from the Elite students of Norlington School for Boys (LONDON).

[patrickJMT]

@akbar2k7 glad to help.

i am going to london to live for a few months in 2011... very excited about it.

[Wafflesistas]

Wow! very simple. I wish that maybe you could explain the rest of the variables and exponents for me. Maybe it is in another video?

[BoomBoomChicky]

saved my Football career

[coldicce]

you're just a lifesaver dude.......thxs

[HearTheBlue]

you're really great patrick. youve gottten me through so many math questions :)

[lissienicole]

this was sooooooo helpful,

thank you so much :)

[amyyanwatse]

thank you so much! this is so useful to me:) I missed a lesson at school, & now need to catch-up on this on my own before the next lesson! reading from the textbook was far too complicated, thanks for the demonstrations:)

[jigsaw7asian]

thxs really neat how it works!!! studying for my high school quiz on this...not a big deal because its a quiz..but a grade is a grade!! really cool stuff!

[bopeepp]

Thanks! I'm studying for my placement test at university, and in the months of relaxation since hs graduation I've forgotten lots of functions and tips and all sorts.. your videos are really helping me get them back!

[buryitiwontletyou]

so much help thank you!

[Cybermouse1992]

you helped me so much with all ur videos! your voice is so clear and your handwritting is pretty neat. Thx bud

[metalbloodshed]

Damn man you make the most helpful videos I've come across and your voice is nice.. no homo lol.

[K1RAN66]

how would you answer a question like

Find the coefficient of x^3 in the expansion of (3-2x)^5

Cheers

[mzmzzzy]

Great thanks!!!

[neworldesign3]

how come n=0, n=1 and n=3 are not worthy of a colon?

[GR1o6180339887498948]

Do you have an easy method for the multinational theorem?

[California292292]

wow, you posted this video the day we started doing this in our math class. O.o

[pabloMTv]

hmm for some reason i did find this pretty neat lol, 5/5!

[tomthecool]

This seems very strange to me that they teach you the n!/(n-r)!r! formula BEFORE showing you Pascal's triangle, over in America!

I was taught about this triangle first, which leads on to a proof of the formula. That makes much more sense.

[gremlinextreme101]

no the proof of the triangle is based on lattice movements using that formula rather than the other way around. Imagine you can only move left or right diagonally down the triangle. The number at a point in the triangle corresponds to the number of different combinations of moves you can make to reach that spot. eg. to reach the 4th row 1st col, we can go lllr, llrl, lrll, or rlll. This is 4 different ways, so 4C2 = 4 which corresponds to the coefficient A^1B^3, or

4!/(4-1)!1!

[macniel1231]

cool stuff! I never knew that the pascal triangle can be used for something besides of fractals. Thank you very much!

[btkw]

What is (a+b)^800?

[cheetah219]

use a computer like he said lol. im sure you can find a java applet for pascal triangles on the internet somewher

[Beorque00]

Do you have a video about series and sequence?...

[patrickJMT]

i have a whole playlist...

[ZamuraiCris]

i've seen that shortcut before, very excellent.

[mentor32]

Damn! I swear you've got some kinda mathematical hard drive in your brain. Is there anything you don't know bro. LOL

Thanx

[br8knight]

thanks

[cyberprodigy]

This one was excelent! Cool shortcut to know.