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

  • Context: MHB 
  • Thread starter Thread starter anemone
  • Start date Start date
  • Tags Tags
    Algebra Challenge
Click For Summary
SUMMARY

The discussion centers on the factorization of the algebraic expression $x^4+y^4+z^4-xyz(x+y+z)$. Initially, a user posted an incorrect problem statement but later clarified that the goal is to find the sum of square factorization for the expression. The correct approach involves recognizing the structure of the polynomial and applying algebraic identities to simplify it effectively.

PREREQUISITES
  • Understanding of polynomial factorization techniques
  • Familiarity with algebraic identities
  • Knowledge of symmetric polynomials
  • Basic skills in manipulating algebraic expressions
NEXT STEPS
  • Study the factorization of symmetric polynomials
  • Learn about the sum of squares in algebra
  • Explore advanced algebraic identities and their applications
  • Practice solving similar algebraic equations for better comprehension
USEFUL FOR

Students of mathematics, algebra enthusiasts, and educators looking to deepen their understanding of polynomial factorization and algebraic identities.

anemone
Gold Member
MHB
POTW Director
Messages
3,851
Reaction score
115
Factorize $x^4+y^4+z^4-xyz(x+y+z)$.
 
Mathematics news on Phys.org
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.
 

Similar threads

MHB Prove Divisibility: $(x-y)^2+(y-z)^2+(z-x)^2=xyz$ yields $x^3+y^3+z^3$
  • · Replies 1 ·
Replies
1
Views
2K
MHB Challenge Problem #7: Σ(x/(y^3+2))≥1
  • · Replies 2 ·
Replies
2
Views
2K
MHB Inequality involves radical, square and factorial expression 3√{x}+2y+1z^2⩽ 13
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Adding 'z' to 2D graph equation
  • · Replies 3 ·
Replies
3
Views
2K
MHB What is the Sum of x, y, and z in a Non-Negative Real Number System?
  • · Replies 4 ·
Replies
4
Views
2K
MHB Show x³y+y³z+z³x is a constant
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad ##x\lt y \lt z## positive integer numbers and if ##\dfrac 1x+\dfrac 1y+\dfrac 1z=\dfrac 13##
  • · Replies 6 ·
Replies
6
Views
2K
MHB Inequality Challenge: Prove $x^2+y^2+z^2\le xyz+2$ [0,1]
  • · Replies 2 ·
Replies
2
Views
2K
MHB Factorize 6(x^5+y^5+z^5)-5(x^2+y^2+z^2)(x^3+y^3+z^3)
  • · Replies 1 ·
Replies
1
Views
1K
MHB Prove Inequality For $x,y,z>0$ When $xyz=1$
  • · Replies 6 ·
Replies
6
Views
2K