第十四集团军撤销:预备班的因式分解

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1.X*X+Y*Y+Z*Z+2XY-2XZ-2YZ-X*X*Y*Y
江户川_新一:怎做的
chinasunsunsun:z(z-2x-2y)=z*z-z(x+y-xy)-z(x+y+xy)如何理解?

X*X+Y*Y+Z*Z+2XY-2XZ-2YZ-X*X*Y*Y
=(x+y)(x+y)-(x*y)(x*y)+z(z-2x-2y)
=(x+y-xy)(x+y+xy)+z*z-z(x+y-xy)-z(x+y+xy)
=(x+y-xy-z)(x+y+xy-z)

(xy-x-y+z)(z-xy-x-y)