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MathGroup Archive 2002

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Re: Simplify

  • To: mathgroup at
  • Subject: [mg32658] Re: [mg32652] Simplify
  • From: Andrzej Kozlowski <andrzej at>
  • Date: Sat, 2 Feb 2002 01:19:33 -0500 (EST)
  • Sender: owner-wri-mathgroup at

First of all, you need to be careful how you enter your products. The 
product of a and b must be entered as a b not ab. Secondly you need some 
conditions on a and b because your answer is not valid in general. So:

Simplify[(a^(1/3) - b^(1/3))*
    ((a^(2/3) + (a*b)^(1/3) + b^(2/3))/(a - b))^(1/3),
   {a >= 0, b >= 0, a >= b}]

(a^(1/3) - b^(1/3))^(2/3)

To see that the conditions are needed just put a=1 and b=2.

N[(a^(1/3) - b^(1/3))*((a^(2/3) + (a*b)^(1/3) + b^(2/3))/
       (a - b))^(1/3) /. {a -> 1, b -> 2}]

-0.20364057097378715 - 0.3527158154089352*I

N[(a^(1/3) - b^(1/3))^(2/3) /. {a -> 1, b -> 2}]

-0.20364057097378704 + 0.35271581540893543*I

Mathematica can't show you how to obtain these solutions. It is not 
designed for that purpose. There is at least one Mathematica based 
program ( Physica) that does that sort of thing (in a limited way of 
course)  but I do not know if there is a way to get it short of becoming 
a physics student at the Open University in England.

Andrzej Kozlowski
Toyama International University

On Saturday, February 2, 2002, at 06:10  AM, simba_leo wrote:

> Hello
> How can I simplify the following term?
> (a^(1/3) - b^(1/3)) * ((a^(2/3) + (ab)^(1/3) + b^(2/3))/(a-b))^(1/3)
> If I use the commands "Simplify", "FullSimplify", "Expand" or 
> "PowerExpand"
> mathematica doesn't find the solution.
> The solution is (a^(1/3)-b^(1/3))^(2/3)
> If it's possible to find the solution in mathematica could mathematica 
> show
> me the way this solution?
> Thanks for your answers!

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