Express x⁴ + y⁴ + z⁴ - 2y²z² - 2z²x² - 2x²y² as the product of four factors.

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SUMMARY

The expression x⁴ + y⁴ + z⁴ - 2y²z² - 2z²x² - 2x²y² can be factored into the product of four linear factors: (x - y - z)(-x + y - z)(-x - y + z)(x + y + z). This factorization is confirmed as correct and provides a clear method for expressing the polynomial in a simplified form. The solution demonstrates the application of algebraic identities and factorization techniques.

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Homework Statement



Express [tex]x^4 + y^4 + z^4 - 2y^2z^2 - 2z^2x^2 - 2x^2y^2[/tex] as the product of four factors.


2. The attempt at a solution

[tex](x-y-z)(-x+y-z)(-x-y+z)(x+y+z)[/tex]
 
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If you really just want someone to check, that works fine.
 
Ok, thanks!
 

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