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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...

(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)

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。

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^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^...

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

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

一.12xyz-9xy =3xy(4z-3y) 二.-x+xy-xz =-x(x-y+z) 三.p(x-y)+q(y-x) =p(x-y)-q(x-y) =(x-y)(p-q) 四.2a(b-c)-3b(c-b) =2a(b-c)+3b(b-c) =(b-c)(2a+3b) 五6(2a+b)(2a-3b)-3(b+2a) =3(2a+b)[2(2a-3b)-3] =3(2a+b)(4a-6b-3) 六.12a(x+y)-18b...

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