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Solving finite difference

  1. Aug 2, 2005 #1
    I am finding (▲^2 - x▲)(x^3).

    I hope I am correct here...

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

    Is my solution correct?
     
  2. jcsd
  3. Aug 2, 2005 #2

    HallsofIvy

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    No. Δ2x3 IS Δ(Δ x3)= Δ((x+1)3- x3)= Δ(3x2+ 3x+ 1)=
    3(x+1)2+ 3(x+1)+ 1- (3x2+ 3x+ 1)= 6x+ 6.
     
    Last edited: Aug 2, 2005
  4. Aug 2, 2005 #3

    Hurkyl

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    The work looks right, but you had really ought to simplify the expression. (Oh, and you need to stick an extra parenthesis in front)
     
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