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

[anemone]

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

 

[kaliprasad]

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

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

Spoiler

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

 

[anemone]

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

Spoiler

$x^4+y^4+z^4-xyz(x+y+z) = x^4-x^2yz - xyz(y+z) + y^4+z^4$ 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!

 

[kaliprasad]

needs closure.