因式分解x^2y-y^2z+z^2x-x^2z+y^2x+z^2y-2xyz

l163 1年前 已收到2个回答 举报
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锻炼身体好 幼苗

共回答了11个问题采纳率：100% 举报

X^2Y-Y^2Z+Z^2X-X^2Z+Y^2X+Z^2Y-2XYZ
=X^2Y+Y^2X-Y^2Z+Z^2Y-XYZ+Z^2X-X^2Z-XYZ
=XY(X+Y)+YZ(Z-Y-X)+XZ(Z-X-Y)
=XY(X+Y)+Z(Z-X-Y)(X+Y)
=(X+Y)[XY+Z(Z-X-Y)]
=(X+Y)(XY+Z^2-ZX-ZY)
=(X+Y)(Z^2-ZX+XY-ZY)
=(X+Y)[Z(Z-X)+Y(X-Z)]
=(X+Y)(X-Z)(Y-Z)
希望是对的.

1年前

4

陈扁 幼苗

共回答了1个问题 举报

X^2Y-Y^2Z+Z^2X-X^2Z+Y^2X+Z^2Y-2XYZ
=X^2Y+Y^2X-Y^2Z+Z^2Y-XYZ+Z^2X-X^2Z-XYZ
=XY(X+Y)+YZ(Z-Y-X)+XZ(Z-X-Y)
=XY(X+Y)+Z(Z-X-Y)(X+Y)
=(X+Y)[XY+Z(Z-X-Y)]
=(X+Y)(XY+Z^2-ZX-ZY)
=(X+Y)(Z^2-ZX+XY-ZY)
=(X+Y)[Z(Z-X)+Y(X-Z)]
=(X+Y)(X-Z)(Y-Z)

1年前

1
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