Question

[(y-z)平方/(x-y)(x-z)]+[(z-x)平方/(y-z)(y-x)]+[(x-y)平方/(z-x)(z-y)]化简

Answer 1

(a-b)^3=a^3-b^3-3a^2b+3ab^2
[(y-z)平方/(x-y)(x-z)]+[(z-x)平方/(y-z)(y-x)]+[(x-y)平方/(z-x)(z-y)]
=[(y-z)^2(y-z)-(z-x)^2(x-z)+(x-y)^2(x-y)]/[(x-y)(x-y)(y-z)]
=[(y-z)^3+(z-x)^3+(x-y)^3]/[(x-y)(x-z)(y-z)]
=-3

追问

为什么知道=[(y-z)^3+(z-x)^3+(x-y)^3]/[(x-y)(x-z)(y-z)]
就可以得出最后答案了？

追答

=(y-z)^3+(z-x)^3+(x-y)^3
=(y^3-z^3-3y^2z+3yz^2)+(z^3-x^3-3z^2x+3zx^2)+(x^3-y^3-3x^2y+3xy^2)
=-3y^2z+3yz^2-3z^2x+3zx^2-3x^2y+3xy^2
=-3[(x-y)(x-z)(y-z)]