Solving finite difference

  • #1
irony of truth
90
0
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
Science Advisor
Homework Helper
43,021
970
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:
  • #3
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,967
19
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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