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因式分解:(y+z)(x+z)(x+y)+xyz

您好: (X+Y)(X+Z)(Y+Z)+XYZ =(X2+XY+XZ+YZ)(Y+Z)+XYZ =(X2Y+XY2+XYZ+Y2Z+X2Z+XYZ+XZ2+YZ2)+XYZ =(X2Y+X2Z+XYZ)+(Y2Z+XY2+XYZ)+(XZ2+YZ2+XYZ) =X(XY+XZ+YZ)+Y(XY+XZ+YZ)+Z(XY+XZ+YZ) =(X+Y+Z)(XY+XZ+YZ) ~如果你认可我的回答,请及时点击【采纳...

因式分解的定义:把一个多项式分解成几个整式的积的形式叫多项式的因式分解。 因为 xyz是单项式,不是多项式。 所以 xyz不能再分解因式了。

x^2(y+z)+y^2(z+x)+z^2(x+y)-(x^3+y^3+z^3)-2xyz =x^2(y+z)+y^2*z+y^2*x+z^2*x+z^2*y-x^3-y^3-z^3-2xyz =x^2(y+z-x)+x(y^2+z^2-2yz)+(y^2*z+z^2*y-y^3-z^3) =x^2(y+z-x)+x(y-z)^2+[y^2(z-y)-z^2(z-y)] =x^2(y+z-x)+x(y-z)^2+(y+z)(y-z)(z-y) =x^...

x2y-y2z+z2x-x2z+y2x+z2y-2xyz=(y-z)x2+(z2+y2-2yz)x+z2y-y2z=(y-z)x2+(y-z)2x-yz(y-z)=(y-z)[x2+(y-z)x-yz]=(y-z)(x+y)(x-z).故选A.

x^2y-y^2z+z^2x-x^2z+y^2x+z^2y-2xyz =y(x^2-2xz+z^2)+(y^2x-y^2z)-(x^2x-z^2z) =y(x-z)^2+y^2(x-z)-xz(x-z) =(x-z)(xy-yz+y^2-xz) =(x-z)[x(y-z)+y(y-z)] =(x-z)(y-z)(x+y)

你好: x²y-y²z+z²x-x²z+y²x+z²y-2xy =(y-z)x²+(z²+y²-2yz)x+z²y-y²z =(y-z)x2²+(y-z)²x-yz(y-z) =(y-z)[x²+(y-z)x-yz] =(y-z)(x+y)(x-z)

题目最好手写,你说的完全读不出因式

x²y+y²x²+x²z-2xyz+x²y =xy(x+xy+xz-2z+x) =xy(2x+xy+xz-2z)

至少是齐次的,即第四项是三次单项式, 但即使是三次,也不好分解因式。

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