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Math Help - Coefficient of x^3 in (1-3x)(1+2x)^6

  1. #1
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    Coefficient of x^3 in (1-3x)(1+2x)^6

    how to solve (1-3x)(1+2x)^6?find the coefficient of term x^3 ..

    thanks a lot ..
    Last edited by mr fantastic; August 23rd 2010 at 12:42 PM. Reason: Useless post title.
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  2. #2
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    Quote Originally Posted by jaycee View Post
    how to solve (1-3x)(1+2x)^6?find the coefficient of term x^3 ..

    thanks a lot ..
    (1+2x)^6=\sum^{n}_{r=0}(6Cr)(2x)^r

    (1-3x)(1+2x)^6=\sum^{n}_{r=0}(6Cr)(2x)^r-\sum^{n}_{r=0}(6Cr)2^kx^{k+1}

    so for the first part put r=3 and the second part put r=2.
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  3. #3
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    Hello, jaycee!

    You could simply crank out the multiplication . . .



    (1-3x)(1+2x)^6

    \text{Find the coefficient of }x^3

    (1 + 2x)^6 \;=\;{6\choose6}1 + {6\choose5}(2x) + {6\choose4}(2x)^2 + {6\choose3}(2x)^3 + \hdots

    . . . . . . . . =\;1 + 12x + 60x^2 + 160x^3 + \hdots


    (1-3x)(1+2x)^6 \;=\;(1-3x)(1 + 12x + 60x^2 + 160x^3+ + \hdots)

    . . . . . . . . . . . . . =\; 1 + 12x + 60x^2 + 160x^3 + \hdots
    . . . . . . . . . . . . . . . . . -\;3x - 36x^2 - 180x^3 - 480x^4 - \hdots

    . . . . . . . . . . . . . =\;1 + 9x + 24x^2 - 20x^3 + \hdots


    Answer: . -20
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  4. #4
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    Talking thank you

    Quote Originally Posted by Soroban View Post
    Hello, jaycee!

    You could simply crank out the multiplication . . .




    (1 + 2x)^6 \;=\;{6\choose6}1 + {6\choose5}(2x) + {6\choose4}(2x)^2 + {6\choose3}(2x)^3 + \hdots

    . . . . . . . . =\;1 + 12x + 60x^2 + 160x^3 + \hdots

    (1-3x)(1+2x)^6 \;=\;(1-3x)(1 + 12x + 60x^2 + 160x^3+ + \hdots)

    . . . . . . . . . . . . . =\; 1 + 12x + 60x^2 + 160x^3 + \hdots
    . . . . . . . . . . . . . . . . . -\;3x - 36x^2 - 180x^3 - 480x^4 - \hdots

    . . . . . . . . . . . . . =\;1 + 9x + 24x^2 - 20x^3 + \hdots


    Answer: . -20
    thanks alott !
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  5. #5
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    thanks !
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