(x+y-z)^2-(x-y+z)^2=?

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(x+y-z)^2-(x-y+z)^2=?
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(x+y-z)^2-(x-y+z)^2=?
(x+y-z)^2-(x-y+z)^2=?

(x+y-z)^2-(x-y+z)^2=?
根据公式(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ac公式展开：
得到(x^2+y^2+z^2=2xy-2yz-2xz)-(x^2+y^2+z^2-2xy-2yz+2xz)
合并同类项,最后得到4xy-4xz

原式=（x+y-z+x-y+z）（x+y-z-x+y-z）
=2x*2y
=4xy

X

(x+y-z)^2-(x-y+z)^2
=[(x+y-z)+(x-y+z)][(x+y-z)-(x-y+z)]
=(2x)(2y-2z)
=4xy-4xz

(x+y-z)^2-(x-y+z)^2=(（x+y）-z)^2-(（x-y）+z)^2=(x+y)^2-2(x+y)z+z^2-((x-y)^2+2(x-y)z+z^2)=x^2+y^2+2xy-2xz-2yz+z^2-x^2-y^2+2xy-2xz+2yz-z^2=4xy-4xz

我告诉你方法，你自己算一下，试子化为：[(x+y)-z]的平方-[(x-y)+z]的平方，
再用完全平方公式打开，打开以后(x+y)的平方和(x-y)的平方同样打开，
再消去相同的项，得结果
解题的关键是把3个项其中的其中两个看作一个

原式=[（x+y-z)+(x-y-z）]×[（x+y-z)-(x-y-z）]
=[x+y-z+x-y-z]×[x+y-z-x+y+z]
=(2x-2z)×2y
=4xy-4yz

(x+y-z)^2-(x-y+z)^2
=(x+y-z+x-y+z)(x+y-z-x+y-z)
=2x*(2y-2z)
=4xy-axz

原式=（x+y-z+x-y+z）（x+y-z-x+y-z） =2x*2y =4xy

(X+Y-Z)^2-(X-Y+Z)^2=(X+Y-Z)(X+Y-Z)-(X-Y+Z)(X-Y+Z) =(X^2+XY-XZ+XY+Y^2-YZ-XZ-YZ+Z^2 )-(X^2-XY+XZ-XY+Y^2-YZ+XZ- -YZ+Z^2 ) =(X^2+Y^2+Z^2+2XY-2XZ-2YZ)-(X^2+Y^2+Z^2-2XY+2XZ-2YZ) =4XY-4XZ

原式=（x+y-z+x-y+z）（x+y-z-x+y-z） =（2x）（2y-2z） =4xy-4xz

用行列式的性质证明：y+z z+x x+y x y z x+y y+z z+x =2 z x y z+x x+y y+z y z x 这个怎么证? (x-2y+z)(x+y-2z)分之（y-x)(z-x) + (x+y-2z)(y+z-2x)分之(z-y)(x-y) + (y+z-2z)(x-2y+z)分之（x-z)(y-z)=?第三部分那个是 （y+z-2x)(x-2y+z)分之（x-z)(y-z) 试证明(x+y-2z)+(y+z-2x)+(z+x-2y)=3(x+y-2z)(y+z-2x)(z+x-2y) 已知：x^2/(z+y)+y^2/(x+z)+z^2/(x+y)=0,求x/(z+y)+y/(x+z)+z/(x+y)的值. x^2/(z+y)+y^2/(x+z)+z^2/(x+y)=0,求x/(z+y)+y/(x+z)+z/(x+y)的值 已知(x+y)(x+z)=x,(y+z)(y+x)=2y,(z+x)(z+y)=3z,求x,y,z (x+y-z)^2-(x-y+z)^2=? (x-y-z)*( )=x^2-(y+z)^2 填空 化简(y-x)(z-x)/(x-2y+z)(x+y-2z)+（z-y)(x-y)/(x-2z+y)(y+z-2x)+(x-z)(y-z)/(y+z-2x)(x-2y+z) 计算:(y-x)(z-x)/(x-2y+z)(x+y-2z)+(z-y)(x-y)/(x+y-2z)(y+z-2x)+(x-z)(y-z)/(y+z-2x)(x-2y+z) 分解因式:f(x,y,z)=x^2(y-z)+y^2(z-x)+z^2(x-y) 证明 ：x/(y+z)+y/(z+x)+z/(x+y)>=3/2其中 x,y,z>0 计算:x^2/(x-y)(x-z)+y^2/(y-x)(y-z)+z^2/(z-x)(z-y) x+2y=3x+2z=4y+z 求x:y:z x+y/2=z+x/3=y+z/4 x+y+z=27 若x+y+z=3y=2z,则x/x+y+z=? x+y+z=14 7z=x+y+2 x+z=y x/2=y/3=z/5 x+3y-z/x-3y+z