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

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1. Nnesha

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

2. Nnesha

|dw:1440509714716:dw|

3. Nnesha

|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

4. Nnesha

let me know if you hve any question cuz i think i didn't explain it clearly

5. anonymous

Wait... I didn't even know there was a formula...

6. anonymous

So how does the formula apply to the triangle?

7. Nnesha

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

8. 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

9. Nnesha

do you know how to solve that^^?

10. anonymous

Ummm... yes?

11. Nnesha

no?

12. Nnesha

4!= 4 times 3 times 2 times 1 so 3!= ???

13. Nnesha

try it! :=)

14. anonymous

Hmmm. solve 3! ?

15. Nnesha

yeh 3! equal to what how would you expand 3! ?

16. anonymous

3*2*1

17. Nnesha

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

18. Nnesha

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

19. Nnesha

$$\color{blue}{\text{Originally Posted by}}$$ @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

20. anonymous

You get 4? Now I am confused...

21. Nnesha

what did you get ?? :(

22. Nnesha

|dw:1440513870886:dw|

23. anonymous

Ohh... 4th term... I got 6... I looked at the 3rd term.

24. Nnesha

yeah i didn't know that either that's why i said 6 but it starts from 0

25. Nnesha

|dw:1440514055424:dw|

26. anonymous

Oh... oops.

27. Nnesha

so you can find coefficients of binomial by using that formula or remember the pattern :=)

28. anonymous

Ok, Thanks. I think I get it.

29. Nnesha

np :=)