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Math Help - Coeffcient in an Expansion

  1. #1
    acc
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    Coeffcient in an Expansion

    In the expansion of (x2 x)8 find the coefficient of x8.
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  2. #2
    MHF Contributor
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    Well, do it! What is your plan?

    <br />
(x^{2}-x)^{8} = \left(x^{2}\right)^{8} + 8\left(x^{2}\right)^{7}(-x) + ...???

    Fill in the ??? and pick out the right one. You can learn to write down specific terms as your NEXT assignment.

    Of course, it might be easier on this one...

    x^{8}\cdot (x - 1)^{8} = x^{8}\cdot\left[x^{8} + 8x^{7}(-1) + ...???\right]
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  3. #3
    Flow Master
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    Quote Originally Posted by acc View Post
    In the expansion of (x2 – x)8 find the coefficient of x8.
    The general term is {8 \choose r} (x^2)^{8 - r} (-x)^r = {8 \choose r} (-1)^r x^{16 - r}. You require the coefficient of the power of x corresponding to 16 - r = 8 ....
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