- #1
MorallyObtuse
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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]
The expression being factored is x⁴ + y⁴ + z⁴ - 2y²z² - 2z²x² - 2x²y².
There are four factors in the final product.
The first factor is (x² + y² + z²).
The second factor is (x² + y² - 2yz).
The third factor is (x² + z² - 2xz).