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Math Help - binomial expansion

  1. #1
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    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
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  2. #2
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    where did you get 70 from?
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    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.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by bobchiba View Post
    where did you get 70 from?
    Do you know the formula for binomial distribution? do you know pascal's triangle?
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    I know what pascals triangle is but i can't say im used to implementing it
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    Re:

    RE:

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    Quote Originally Posted by bobchiba View Post
    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)
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  8. #8
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    Re:

    Maybe, Maybe not...I am beginning to wonder myself what happened to "e"
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  9. #9
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    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
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    Re:

    RE:

    I worked the problem out by hand and kept getting this...
    Attached Thumbnails Attached Thumbnails binomial expansion-expansion-2.gif  
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  11. #11
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    thats the answere in the text book, yes
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  12. #12
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    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!
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  13. #13
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    It is easy!
    Attached Thumbnails Attached Thumbnails binomial expansion-biuon.gif  
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  14. #14
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by bobchiba View Post
    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?

    now try your question again and tell me your answer
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    is up to his old tricks again! Jhevon's Avatar
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    As you see from Plato's post, you have to know what factorials are to use the Binomial expansion method, you can do it that way as well...you do know what factorials are right?

    Both the methods are easy to learn and easy to implement and i use both depending on what i want. Pascal's triangle i use to expand smaller binomial expansions, say where the highest power is like 6,7, or maybe 8. i use the binomial expansion method when dealing with higher powers

    one advantage of the Binomial expansion method however, is that you can tell what any term is right of the bat.

    say for instance we ONLY want the 17th term of (x + 6)^28
    with Pascal's triangle method you would need to more or less calculate all the coefficients before that, not to mention draw Pascal's triangle to line 17. with the binomial expansion method, the answer is immediate, as Plato illustrated
    Last edited by ThePerfectHacker; May 5th 2007 at 05:05 PM.
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