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（x^4+y^4+z^4-2x^2y^2-2x^2z^2-2y^2z^2)/(x+y+z)
题目详情
（x^4+y^4+z^4-2x^2y^2-2x^2z^2-2y^2z^2)/(x+y+z)
▼优质解答
答案和解析
(x^4+y^4+z^4-2x^2y^2-2x^2z^2-2y^2z^2)/(x+y+z)
=(x^4+y^4+z^4-2x^2y^2-2x^2z^2+2y^2z^2-4y^2z^2)/(x+y+z)
=[(x^2-y^2-z^2)^2-4y^2z^2]/(x+y+z)
=[(x^2-y^2-z^2+2yz)(x^2-y^2-z^2-2yz)]/(x+y+z)
=(x+y+z)(x+y-z)(x+z-y)(x-y-z)/(x+y+z)
=(x+y-z)(x+z-y)(x-y-z)
=(x^4+y^4+z^4-2x^2y^2-2x^2z^2+2y^2z^2-4y^2z^2)/(x+y+z)
=[(x^2-y^2-z^2)^2-4y^2z^2]/(x+y+z)
=[(x^2-y^2-z^2+2yz)(x^2-y^2-z^2-2yz)]/(x+y+z)
=(x+y+z)(x+y-z)(x+z-y)(x-y-z)/(x+y+z)
=(x+y-z)(x+z-y)(x-y-z)
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