x的三次方-8y的三次方-z的三次方-6xyz

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/29 16:26:48
x的三次方-8y的三次方-z的三次方-6xyz

x的三次方-8y的三次方-z的三次方-6xyz
x的三次方-8y的三次方-z的三次方-6xyz

x的三次方-8y的三次方-z的三次方-6xyz
x3-8y3-z3-6xyz
=x^3-3x^2z+3xz^2-z^3-8y^3-6xyz+3x^2z-3xz^2
=(x^3-3x^2z+3xz^2-z^3)-8y^3+(3x^2z-3xz^2-6xyz)
=(x-z)^3-(2y)^3+3xz(x-z-2y)
=(x-2y-z)[(x-z)^2+2y(x-z)+4y^2]+3xz(x-2y-z)
=(x-2y-z)(x^2-2xz+z^2+2xy-2yz+4y^2)+3xz(x-2y-z)
=(x-2y-z)(x^2+4y^2+z^2+2xy+xz-2yz)