Solve Algebraic Equation: x⁴+y⁴+z⁴-xyz(x+y+z)

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Discussion Overview

The discussion revolves around the factorization of the expression $x^4+y^4+z^4-xyz(x+y+z)$. Participants initially engage with the problem of factorization, but it evolves into clarifying the correct formulation of the problem, which involves finding the sum of square factorization.

Discussion Character

  • Debate/contested, Conceptual clarification

Main Points Raised

  • Some participants inquire about the correctness of the original problem statement regarding the factorization of $x^4+y^4+z^4-xyz(x+y+z)$.
  • A participant acknowledges a mistake in the problem formulation and clarifies that the correct problem is to find the sum of square factorization for the expression.
  • Another participant notes that the discussion needs closure, indicating a desire for resolution.

Areas of Agreement / Disagreement

There is no consensus on the original problem as it was initially presented, but a clarification has been made regarding the correct formulation. The discussion remains somewhat unresolved as participants seek closure.

Contextual Notes

The initial confusion stemmed from the incorrect problem statement, which may have led to misunderstandings about the intended mathematical task.

Who May Find This Useful

Participants interested in algebraic factorization, particularly in the context of polynomial expressions and their properties.

anemone
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Factorize $x^4+y^4+z^4-xyz(x+y+z)$.
 
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anemone said:
Factorize $x^4+y^4+z^4-xyz(x+y+z)$.

is the question correct (that is I am missing something)

$x^4+y^4+z^4-xyz(x+y+z) = x^4-x^2yz - xyz(y+z) + y^4+z^4$ if we put in descending power of x and $y^4+z^4$ does not factor over real coefficients
 
kaliprasad said:
is the question correct (that is I am missing something)

$x^4+y^4+z^4-xyz(x+y+z) = x^4-x^2yz - xyz(y+z) + y^4+z^4$ if we put in descending power of x and $y^4+z^4$ does not factor over real coefficients

Ops...it was my mistake to post an incorrect problem...the problem should read:

Find the sum of square factorization for $x^4+y^4+z^4-xyz(x+y+z)$.

Sorry for causing the confusion, folks!:o
 
needs closure.
 

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