因式分解：x^6-y^6+x^4+x^2y^2+y^4_数学解答

因式分解：x^6-y^6+x^4+x^2y^2+y^4

人气：423 ℃　时间：2020-04-27 20:45:26

解答

^6-y^6+x^4+x^2y^2+y^4
=(x^2-y^2)(x^4+x^2y^2+y^4)+(x^4+x^2y^2+y^4)
=(x^2-y^2+1)(x^4+x^2y^2+y^4)
=(x^2-y^2+1)(x^4+2x^2y^2+y^4-x^2y^2)
=(x^2-y^2+1)[(x^2+y^2)^2-x^2y^2]
=(x^2-y^2+1)(x^2+y^2-xy)(x^2+y^2+xy)