Solving finite difference

  • #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?
 

Answers and Replies

  • #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.
 
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  • #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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