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Math Help - Binomail theorem

  1. #1
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    Binomail theorem

    use the binomial theorem to expand and simplify the expression.

    (a-3b)^5

    can someone please explain to me how to use pascal"s triangle? i dont understand how they can just pull a bunch of numbers out of there?
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  2. #2
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    Quote Originally Posted by flexus View Post
    use the binomial theorem to expand and simplify the expression.

    (a-3b)^5

    can someone please explain to me how to use pascal"s triangle? i dont understand how they can just pull a bunch of numbers out of there?
    the coefficients of the expanded form of (x+y)^5 are contained in the 6th row of Pascal's triangle ...

    1 , 5 , 10 , 10 , 5 , 1

    (x+y)^5 = x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5 <br />

    note that the exponents of x start at 5 and decrease to 0 ... and the exponents of y start at 0 and increase to 5.

    now, replace x with a and y with (-3b)

    (a-3b)^5 = a^5 + 5a^4(-3b) + 10a^3(-3b)^2 ... and so on
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  3. #3
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    Quote Originally Posted by skeeter View Post
    the coefficients of the expanded form of (x+y)^5 are contained in the 6th row of Pascal's triangle ...

    1 , 5 , 10 , 10 , 5 , 1

    (x+y)^5 = x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5 <br />

    note that the exponents of x start at 5 and decrease to 0 ... and the exponents of y start at 0 and increase to 5.

    now, replace x with a and y with (-3b)

    (a-3b)^5 = a^5 + 5a^4(-3b) + 10a^3(-3b)^2 ... and so on
    thank you so much for taking you rtime to help me skeeter. but i don't see how you knew to use those numbers? is there anyway you could explain a little more deep. im sorry to ask so much. just don't understand this stuff. when i look at it all i see is a dark forest lol.
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