Question

因式分解：x^2y-y^2z+z^2x-x^2z+y^2x+z^2y-zxyz

如题：因式分解：x^2y-y^2z+z^2x-x^2z+y^2x+z^2y-zxyz
注：x^2表示x的平方
求解，谢谢，需详细解题步骤

Answer 1

x^2y-y^2z+z^2x-x^2z+y^2x+z^2y-2xyz

=(x2y-x2z)+(z2y-y2z)+<(xy2+xz2)-2xyz>
=x2(y-z)-yz(y-z)+<x(y2+z2)-2xyz>
=(y-z)(x2-yz)+x(y2-2yz+z2)
=(y-z)(x2-yz)+x(y-z)(y-z)
=(y-z)(x2-yz+xy-xz)
分组分解法，只是分组有点难，主要是寻找与公式有关的项分到一组去。

Answer 2

原式=(x2y-x2z)+(z2y-y2z)+<(xy2+xz2)-2xyz>
=x2(y-z)-yz(y-z)+<x(y2+z2)-2xyz>
=(y-z)(x2-yz)+x(y2-2yz+z2)
=(y-z)(x2-yz)+x(y-z)(y-z)
=(y-z)(x2-yz+xy-xz)

Answer 3

X