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Is my text book messing wih me again?

  1. May 19, 2007 #1
    Here is an example in my book...

    Determine the coefficient of x^6 in the expansion of

    (2-3x^2)(1+2x)^8


    (2-3x^2)(1+2x)^8 = 2(1+2x)^8 - 3x^2(1+2x)^8

    The general term in the expansion of (1+2x)^8 is

    C(8,k)(2x)^k

    Therefore, the term containing x^6 in the expansion of (2-3x^2)(1+2x)^8 is

    2(C(8,6))(2x)^6 - 3x^2(C(8,4))(2x)^4 = 2(2^6)(C(8,6))(x^6) - 3(2^4)(C(8,4))(x^6) = 224x^6

    The coefficient is 244

    Where the heck did these 4's come from??? Shouldn't they be 6's or am I missing something?
     
    Last edited: May 19, 2007
  2. jcsd
  3. May 19, 2007 #2

    cristo

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    You're looking for the coefficient of x^6. In the first term, this will be equal to the coefficient of x^6, but the second term is premultiplied by x^2, thus to obtain the coefficient of x^6 in this term, you must look at the term x^4 in the expansion of (1+2x)^8 [since x^2.x^4=x^6]
     
  4. May 19, 2007 #3
    Saved again, thanks Cristo
     
  5. May 19, 2007 #4

    cristo

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    You're welcome.
     
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