x^3+y^3+z^3-3xyz(分解因式)3 3 3X + Y +Z -3XYZ(分解因式)X的3次+Y的3次+Z的3次-3XYZ
问题描述:
x^3+y^3+z^3-3xyz(分解因式)
3 3 3
X + Y +Z -3XYZ(分解因式)
X的3次+Y的3次+Z的3次-3XYZ
答
x^3+y^3+z^3-3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)
由x^3+y^3+z^3=(x+y+z)(x^2+y^2+z^2)-z(x^2+y^2)-x(y^2+z^2)-y(x^2+z^2)
x^3+y^3+z^3-3xyz=……=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)
答
x^3+y^3+z^3-3xyz
=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)