1. ## binomial expansion

Hi there,

Does anyone know of an easy to remember way of expanding binomials, I do have a grasp of it but wondering if theres a better way of doing it?

An example would be (e + f)^5

2. where did you get 70 from?

3. ## Re:

I used a computer to do this, because I feel that asking me to expand anything above (a+b)^3 is a complete waste of my time.

4. Originally Posted by bobchiba
where did you get 70 from?
Do you know the formula for binomial distribution? do you know pascal's triangle?

5. I know what pascals triangle is but i can't say im used to implementing it

6. ## Re:

RE:

7. Originally Posted by bobchiba
I know what pascals triangle is but i can't say im used to implementing it
i guess what i'm really asking is, by what method did you learn to do this in class, by the binomial expansion method or the Pascal's triangle method, so i know which method to explain to you to show you how qbkr21 got a 70 (which i assume is correct since he used his pc to do it, but i haven't checked)

8. ## Re:

Maybe, Maybe not...I am beginning to wonder myself what happened to "e"

9. well the triangle i have is different,

1 3 3 1
1 4 6 4 1
1 5 10 10 5 1 (not complete) sort of looks similar to this,

and i just have to expand it, not solve it

10. ## Re:

RE:

I worked the problem out by hand and kept getting this...

11. thats the answere in the text book, yes

12. ## Re:

RE:

DO YOU WANT ME TO WORK IT OUT FOR YOU?

If I were you I wouldn't worry about this to much. Beyond this class you will rarely if ever be asked to this...Good Luck!

13. It is easy!

14. Originally Posted by bobchiba
well the triangle i have is different,

1 3 3 1
1 4 6 4 1
1 5 10 10 5 1 (not complete) sort of looks similar to this,

and i just have to expand it, not solve it
it's the same triangle, it's just that one is a right-triangle and the other is an isoselese...um...yeah, so anyway...

apparently you know the Pascal's triangle method, here's how to implement it.

we have the Pascal's triangle:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

these numbers give the coefficients for all the terms in a binomial expansion. so we place them into position as they are in the triangle. then we take the products of the two terms in the binomials and place them in the following order.

the first power of the first element is the highest power of the expansion, we start at the highest power and count down by 1 until we get to zero. for the second element, we start with power zero and count up till we get to the highest power.

so for say (a + b)^n the terms will have the form, Ca^(n - k)*b^(k), where C is the coefficient given by Pascal's triangle and k = 0,1,2,3...n

so for instance:

(x + 2)^4 = 1*x^4(2)^0 + 4*(x^3)(2^1) + 6*(x^2)(2^2) + 4*(x^1)(2^3) + 1*(x^0)(2^4)

notice that the numbers in front are given by the line of Pascal's triangle where the second number is 4, and that i start with the power of x (the first element) as 4 and count down, and start with the power of 2 (the second element) as 0 and count up

so, (x + 4)^4 = 1x^4 + 4*2*x^3 + 6*4*x^2 + 4*8*x + 1*16
...................= x^4 + 8x^3 + 24x^2 + 32x + 16

do you get it now?