28式枪榴弹发射器:(x+y-z)(x-y+z)-(x-y-z)(x+y+z)

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

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

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

楼上两位，你们都算错啦

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

主要思路：合并使用平方差，消项，移项，展开处理，最后答案是4YZ

这道题等于0

(x-y-z)(x+y+z) (x+y-z)(x-y+z)-(x-y-z)(x+y+z) 已知x,y,z为正实数,y*y=x*z,求证:x*x+y*y+z*z>(x-y+z)*(x-y+z) 正数x,y,z, xyz(x+y+z)=1,则(x+y)(x+z)最小值？ c语言#define M(x,y,z) x*y+z X*X*X+Y*Y*Y=Z*Z*Z 有整数解没? X,Y,Z 不为0 因式分解(x+y+z)^3-(y+z-x)^3-(z+x-y)^3-(x+y-z)^3 已知数x、y、z满足x/y+z + y/z+x +z/x+y=1，求 求(X+2Y-Z)(X-2Y+Z)-(X+2Y+Z) x-y+z=a,x+y-z=b,-x+y+z=c