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

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/27 14:17:24

1.因式分解x^2 y - y^2 z + z^2 x-x^2 z +y^2 x + z^2 y -2xyz
2.x^2 - (m^2 + n^2 ) x +mn (m^2 -n^2 )
3.(c-2 )^2 - 4 (b-c)(a-b)

1.因式分解x^2 y - y^2 z + z^2 x-x^2 z +y^2 x + z^2 y -2xyz
=z^2(x+y)+xy*(x+y)-z(x^2+2xy+y^2)
=z^2(x+y)+xy(x+y)-z(x+y)^2
=(x+y)*(z^2+xy-zx-zy)
=(x+y)[z(z-x)-y(z-x)]
=(x+y)(Z-x)(z-y)
2.x^2 - (m^2 + n^2 ) x +mn (m^2 -n^2 )
=x^2-(m^2+n^2)+[n(m+n)m(m-n)]
=[x-n(m+n)][x-m(m-n)]
=(x-mn-n^2)(x-m^2+mn)
3.(c-2 )^2 - 4 (b-c)(a-b)
=题目对吗?

因式分解 (x+y+z)^2+yz(y+z)+xyz 因式分解：25x y^2 z^2 (x+y-z)-30xyz(z-x-y)^2+5x y z^3 (z-x-y) 因式分解X2(Y+Z)+Y2(Z+X)+Z2(X+Y)-(X3+Y3+Z3)-2XYZ (y-x)/(x+z-2y)(x+y-2z)+(z-y)(x-y)/(x+y-2z)(y+z-2x)+(x-z)(y-z 因式分解 x^2(y+z)+y^2(z+x)+z^2(x+y)-(x^3+y^3+z^3)-2xyz 已知 x,y,z都是正实数,且 x+y+z=xyz 证明 (y+x)/z+(y+z)/x+(z+x)/y≥2(1/x+1 x,y,z正整数 x>y>z证明 x^2x +y^2y+z^2z>x^(y+z)*y^(x+z)*z^(x+y) 化简(y-x)(z-x)/(x-2y+z)(x+y-2z)+（z-y)(x-y)/(x-2z+y)(y+z-2x)+(x (x-2y+z)(x+y-2z)分之（y-x)(z-x) + (x+y-2z)(y+z-2x)分之(z-y)(x-y) 证明已知xyz∈R^+, x^2x * y^2y* z^2z≥x^y+x* y^z+x * z^x+y 3道高数题,1,函数F(x,y,z)=(e^x) * y * (z^2) ,其中z=z(x,y)是由x+y+z+xyz= 化简(y-x)(z-x)/(x-2y+z)(x+y-2z)+（z-y)(x-y)/(xy-2z)(y+z-2x)+(x-