Question

球一到数学题：分解因式：x^4+y^4+z^4-2x²y²-2x²z²+2y&s

Answer 1

x^4+y^4+z^4-2x^2y^2-2y^2z^2-2z^2x^2

=(x^4-2x^2y^2+y^4)+z^4-2y^2z^2+2z^2x^2-4z^2x^2

=(x^2-y^2)^2+2z^2(x^2-y^2)+z^4-4z^2x^2

=(x^2-y^2+z^2)^2-4z^2x^2

=(x^2-y^2+z^2+2zx)(x^2-y^2+z^2-2zx)

=[(x+z)^2-y^2][(x-z)^2-y^2]

=(x+y+z)(x-y+z)(x+y-z)(x-y-z)