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Math Help - a binomial thm problem

  1. #1
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    a binomial thm problem

    a binomial thm problem
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by afeasfaerw23231233 View Post
    a binomial thm problem
    i'm sorry. i don't see a much nicer way to do this problem. i would have done it with brute force like you did
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    Forum Admin topsquark's Avatar
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    (1 + 2x)^4(1- x)^3

    The most clever thing I can come up with is to define two new variables:
    y = 1 + \frac{x}{2}
    and
    z = \frac{3x}{2}

    Then
    y + z = 1 + 2x
    and
    y - z = 1 - x

    Thus
    (1 + 2x)^4(1- x)^3 = (y + z)^4(y - z)^3

    = [(y + z)^3(y - z)^3](y + z)

    = (y^2 - z^2)^3(y + z)

    = ([1 + 2x]^2 - [1 - x]^2)^3(1 + 2x)
    etc.

    But I doubt this actually cuts down on the work load.

    -Dan
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