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Expansion Question

  1. Jan 21, 2007 #1
    1. The problem statement, all variables and given/known data

    Expand:
    (w + x((2t)/T) + y((2t)/T)^2 + z((2t)/T)^3)^2

    I need to expand this expression and have completly forgetten how to go about doing this. Any help would be appreciated. thanks.



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited: Jan 21, 2007
  2. jcsd
  3. Jan 21, 2007 #2

    arildno

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    Would you be able to expand the expression (a+b)^2?
     
  4. Jan 21, 2007 #3
    yes, it is a^2 + 2ab + b^2
     
  5. Jan 21, 2007 #4

    arildno

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    Okay, so you could, for example start with defining a=(w+x(2t/T)+y(2t/T)^2) and b=z(2t/T)^3.

    Can you set up what you get then?
     
  6. Jan 21, 2007 #5
    w^2 + z^2(2t/T)^2 + y^2(2t/T)^4 + 2wz(2t/T)^3 + 2xz(2t/T)^4 + 2yz(2t/T)^6 + z^2(2t/T)^6

    is that correct?
     
  7. Jan 21, 2007 #6

    arildno

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    No, do this PIECEWISE.
    Just insert the expressions (with appropriate parantheses) on the a and b places before doing any further manipulations!
     
  8. Jan 21, 2007 #7
    ok so [(w+x(2t/T)+y(2t/T)^2) + (z(2t/T)^3)]^2 would be (a+b)^2
     
  9. Jan 21, 2007 #8

    arildno

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    Right!
    Use now the expansion formula you just cited for a and b!
     
  10. Jan 21, 2007 #9
    w^2 + 2wx(2t/T) + (x^2+2wy)(2t/T)^2 + (2xy+2wz)(2t/T)^3 + (y^2+2xz)(2t/T)^4 + (2yz+z^2)(2t/T)^6

    Is this right?
     
  11. Jan 21, 2007 #10
    sorry, I think this should be correct now:

    w^2 + 2wx(2t/T) + (x^2+2wy)(2t/T)^2 + (2xy+2wz)(2t/T)^3 + (y^2+2xz)(2t/T)^4 + 2yz(2t/T)^5 + z^2(2t/T)^6

    Is this right?
     
  12. Jan 22, 2007 #11

    arildno

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    Right! :smile:
     
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