How do you apply Pascal's Triangle?

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How do you apply Pascal's Triangle?

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To expand binomials you can apply pascal's triangle like you don't have to apply the binomial formula to solve \[\huge\rm ^4C_3\] just look at the triangle to find the coefficient of the terms 4th row http://www.mathwarehouse.com/animated-gifs/images/pascals-triangle-example-showing-recursion.gif
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|dw:1440509928206:dw| 1+2 =3 (left side) 1+2 =3 right side you can also find these by using \[^nC_r =\frac{ n! }{ r!(n-r)! }\]formula

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let me know if you hve any question cuz i think i didn't explain it clearly
Wait... I didn't even know there was a formula...
So how does the formula apply to the triangle?
tthe numbers in the pascal's triangle are the coefficient of binomial theorem \[\Large\rm(x+y)^4=\color{red}{1}x^4+\color{reD}{4}x^3y+\color{Red}{6}x^2y^2+\color{Red}{4}xy^3+\color{reD}{1}y^4\] here is an example red numbers are the coefficient you can find it by looking at the pascal's triangle or using that formula
let's say we nee 3rd term of 4th row \[^4C_3=\frac{ 4! }{ 3!(4-3)!}\] when you solve this you will get 6
do you know how to solve that^^?
Ummm... yes?
no?
4!= 4 times 3 times 2 times 1 so 3!= ???
try it! :=)
Hmmm. solve 3! ?
yeh 3! equal to what how would you expand 3! ?
3*2*1
yes right \[^4C_3=\frac{\color{green}{ 4!} }{ \color{blue}{3!}\color{reD}{(4-3)!}}\]\[\frac{\color{green}{ 4 \times \cancel{3} \times \cancel{2} \times 1 }}{\color{blue}{\cancel{ 3} \times \cancel{2} \times 1}\color{red}{(1)}!}\] answer would be one
yes right \[^4C_3=\frac{\color{green}{ 4!} }{ \color{blue}{3!}\color{reD}{(4-3)!}}\]\[\frac{\color{green}{ 4 \times \cancel{3} \times \cancel{2} \times 1 }}{\color{blue}{\cancel{ 3} \times \cancel{2} \times 1}\color{red}{(1)}!}\] answer would be 4
\(\color{blue}{\text{Originally Posted by}}\) @Nnesha let's say we nee 3rd term of 4th row \[^4C_3=\frac{ 4! }{ 3!(4-3)!}\] when you solve this you will get 6 \(\color{blue}{\text{End of Quote}}\) my bad i meant you will get 4
You get 4? Now I am confused...
what did you get ?? :(
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Ohh... 4th term... I got 6... I looked at the 3rd term.
yeah i didn't know that either that's why i said 6 but it starts from 0
|dw:1440514055424:dw|
Oh... oops.
so you can find coefficients of binomial by using that formula or remember the pattern :=)
Ok, Thanks. I think I get it.
np :=)

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