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Solving finite difference

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?
 

HallsofIvy

Science Advisor
Homework Helper
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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 by a moderator:

Hurkyl

Staff Emeritus
Science Advisor
Gold Member
14,845
17
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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