# Solving finite difference

#### irony of truth

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?

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#### HallsofIvy

Homework Helper
No. Δ2x3 IS Δ(&Delta; x3)= Δ((x+1)3- x3)= &Delta;(3x2+ 3x+ 1)=
3(x+1)2+ 3(x+1)+ 1- (3x2+ 3x+ 1)= 6x+ 6.

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#### Hurkyl

Staff Emeritus
Gold Member
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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