分解因式:x^4+y^4+z^4－2x^2y^2－2x^2z^2－2y^2z^2_数学解答

分解因式:x^4+y^4+z^4－2x^2y^2－2x^2z^2－2y^2z^2

人气：228 ℃　时间：2020-02-03 07:53:19

解答

原式=
x^4-(2y^2+2z^2)x^2+y^4+z^4-2y^2z^2
=x^4-(2y^2+2z^2)x^2+(y^2-z^2)^2
=x^4-(2y^2+2z^2)x^2+(y+z)^2(y-z)^2
=[x^2-(y+z)^2][x^2-(y-z)^2]
=(x+y+z)(x-y-z)(x+y-z)(x-y+z)