作业帮计算：（X+y+z)(-x+y+z)(x-y+z)(x+y-z)
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/27 16:50:07
计算：（X+y+z)(-x+y+z)(x-y+z)(x+y-z)
计算：（X+y+z)(-x+y+z)(x-y+z)(x+y-z)
计算：（X+y+z)(-x+y+z)(x-y+z)(x+y-z)
=[(y+z)+x][(y+z)-x][x-(y-z)][x+(y-z)]
=[(y+z)^2-x^2][x^2-(y-z)^2]
=(y^2+2yz+z^2-x^2)(x^2-y^2+2yz-z^2)
=[2yz+(y^2+z^2-x^2)][2yz-(y^2+z^2-x^2)]
=4y^2z^2-(y^2+z^2-x^2)^2
=4y^2z^2-x^4-y^4-z^4-2y^2z^2+2x^2y^2+2x^2z^2
=-x^4-y^4-z^4+2x^2y^2+2x^2z^2+2y^2z^2
=-（X+y+z)(x-y-z)(x-y+z)(x+y-z)
=-[(x+y)^2-z^2][(x-y)^2-z^2]
[（X+Y）+Z][(X+Y)-Z][Z+(x-y)][z-(x-y)]
=[(x+y)^2-z^2][z^2-(x-y)^2]
原式=[(y+z)+x]*[(y+z)-x]*[x-(y-z)]*[x+(y-z)]
=[(y+z)^2 - x^2]*[x^2 - (y-z)^2]
=[y^2+z^2+2yz-x^2]*[x^2-y^2-z^2+2yz]
=[2yz+(y^2+z^2-x^2)]*[2yz-(y^2+z^2-x^2)]
=(2yz)^2 - [y^...
全部展开
原式=[(y+z)+x]*[(y+z)-x]*[x-(y-z)]*[x+(y-z)]
=[(y+z)^2 - x^2]*[x^2 - (y-z)^2]
=[y^2+z^2+2yz-x^2]*[x^2-y^2-z^2+2yz]
=[2yz+(y^2+z^2-x^2)]*[2yz-(y^2+z^2-x^2)]
=(2yz)^2 - [y^2+z^2-x^2]^2
=4(yz)^2 - [y^4+z^4+x^4+2(yz)^2-2(xy)^2-2(xz)^2]
=-[x^4+y^4+z^4+2(xy)^2+2(yz)^2+2(xz)^2]
=-(x^2+y^2+z^2)^2
收起