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Math Help - Quick Binomial Expansion question

  1. #1
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    Quick Binomial Expansion question

    What is the coefficient of x3 in this expansion....

    (1-x2)2(1+x)8

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  2. #2
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    Re: Quick Binomial Expansion question

    Quote Originally Posted by sirellwood View Post
    What is the coefficient of x3 in this expansion....

    (1-x2)2(1+x)8

    There is no quick answer unless you use this.
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    Re: Quick Binomial Expansion question

    Before we had that, we had to use this: Binomial theorem - Wikipedia, the free encyclopedia

    So (1-x^2)^2 = 1-2x^2+x^4, and
    (1+x)^8=1+8x+28x^2+56x^3+70x^4+56x^5+28x^6+8x^7+x^  8

    Picking out the x^3 terms gives:
    (1)(56x^3)+(-2x^2)(8x)=56x^3-16x^3=40x^3, so the coefficient we're looking for is 40.

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    Re: Quick Binomial Expansion question

    By observation we can see that the first expansion will have three terms, one will be constant 1, second with x ^2 and third x^4.
    The second expansion will have powers of x from 0 to 8.
    Since we have to multiply and get coefficient of x^3, we need to know first two terms of first expansion i.e., 1 -2x^2 and from the second expansion we need to know terms containing x, and x^3 that is 2nd and fourth term.
    Thus by knowing four terms we can multiply and get the coefficient of x^3.
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