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anonymous
 one year ago
How do you apply Pascal's Triangle?
anonymous
 one year ago
How do you apply Pascal's Triangle?

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Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2To 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/animatedgifs/images/pascalstriangleexampleshowingrecursion.gif

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2dw:1440509928206:dw 1+2 =3 (left side) 1+2 =3 right side you can also find these by using \[^nC_r =\frac{ n! }{ r!(nr)! }\]formula

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2let me know if you hve any question cuz i think i didn't explain it clearly

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wait... I didn't even know there was a formula...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So how does the formula apply to the triangle?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2tthe 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

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2let's say we nee 3rd term of 4th row \[^4C_3=\frac{ 4! }{ 3!(43)!}\] when you solve this you will get 6

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2do you know how to solve that^^?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.24!= 4 times 3 times 2 times 1 so 3!= ???

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2yeh 3! equal to what how would you expand 3! ?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2yes right \[^4C_3=\frac{\color{green}{ 4!} }{ \color{blue}{3!}\color{reD}{(43)!}}\]\[\frac{\color{green}{ 4 \times \cancel{3} \times \cancel{2} \times 1 }}{\color{blue}{\cancel{ 3} \times \cancel{2} \times 1}\color{red}{(1)}!}\] answer would be one

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2yes right \[^4C_3=\frac{\color{green}{ 4!} }{ \color{blue}{3!}\color{reD}{(43)!}}\]\[\frac{\color{green}{ 4 \times \cancel{3} \times \cancel{2} \times 1 }}{\color{blue}{\cancel{ 3} \times \cancel{2} \times 1}\color{red}{(1)}!}\] answer would be 4

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2\(\color{blue}{\text{Originally Posted by}}\) @Nnesha let's say we nee 3rd term of 4th row \[^4C_3=\frac{ 4! }{ 3!(43)!}\] when you solve this you will get 6 \(\color{blue}{\text{End of Quote}}\) my bad i meant you will get 4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You get 4? Now I am confused...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ohh... 4th term... I got 6... I looked at the 3rd term.

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2yeah i didn't know that either that's why i said 6 but it starts from 0

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.2so you can find coefficients of binomial by using that formula or remember the pattern :=)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok, Thanks. I think I get it.
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