Question

因式分解x^4+y^4+z^4-2x^2y^2-2y^2z^2-2z^2x^2

Answer 1

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

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

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

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

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

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

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