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MathGroup Archive 2002

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Re: Simplify

  • To: mathgroup at
  • Subject: [mg32657] Re: Simplify
  • From: "David P. Johnson" <johnson at>
  • Date: Sat, 2 Feb 2002 01:19:32 -0500 (EST)
  • Organization: New Mexico Tech
  • References: <a3f0q2$b3p$>
  • Sender: owner-wri-mathgroup at

In article <a3f0q2$b3p$1 at>, Stich Sebastian
<seb_stich at> 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!

Well, you could learn some algebra. 

The quantity (a^(1/3)-b^(1/3)) does not equal (a-b)^(1/3), so you can't
cancel them. And didn't you mean ((a^(2/3) - 2(a*b)^(1/3) + b^(2/3))?
Even if you did, you can't change that to ((a^2 - 2(a*b) + b^2)^(1/3),
so you can't factor the expression inside the second parentheses. Your
proposed simplification is complete garbage. No wonder Simplify[]
didn't come up with it.

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