x^3+y^3+z^3-3xyz变成(x+y+z)(x^2+y^2+z^2-xy-yz-xz)步骤
问题描述：
x^3+y^3+z^3-3xyz变成(x+y+z)(x^2+y^2+z^2-xy-yz-xz)步骤
答
("是平方"'是三次方)原式=(x"'+y"'+z"'-xyz-xyz-xyz)+xy"-xy"+xz"-xz"+x"y-x"y+x"z-x"z+zy"-zy"+yz"-yz"=(x"'+xy"+xz"-x"y-xyz-x"z)+(x"y+y"'+yz"-xy"-zy"-xyz)+(x"z+zy"+z"'-xyz-yz"-xz")=x(x"+y"+z"-xy-yz-xz)+y(x"+y"+z"-xy-yz-xz)+z(x"+y"+z"-xy-yz-xz)=(x+y+z)(x"+y"+z"-xy-yz-xz)
答
x^3+y^3+z^3-3xyz
=[( x+y)^3-3x^2y-3xy^2]+z^3-3xyz
=[(x+y)^3+z^3]-(3x^2y+3xy^2+3xyz)
=(x+y+z)[(x+y)^2-(x+y)z+z^2]-3xy(x+y+z)
=(x+y+z)(x^2+y^2+2xy-xz-yz+z^2)-3xy(x+y+z)
=(x+y+z)(x^2+y^2+z^2-xy-xz-yz)