作业帮（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：2024/05/04 20:20:16
（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+y+z）*（x-y+z）*（x+y-z）=
（x+y+z）*（-x+y+z）*（x-y+z）*（x+y-z） 因数 1 2 3 4
=（x+y+z）*（x+y-z）*（-x+y+z）*（x-y+z） 将因数1与因数4结合,因数2与因数3结合
= [(x+y)^2-z^2] *{[z-(x-y)][z+(x-y)]} 对因数1和4应用平方公式 （a+b）(a-b)=a^2 -b^2
= [(x+y)^2-z^2] [z^2- (x-y)^2] 再对因数2和3应用平方公式（a+b）(a-b)=a^2 -b^2
= (x^2+2xy+y^2-z^2) [z^2-(x-y)^2]
= - (x^2+y^2-z^2+2xy)(x^2+y^2-z^2-2xy) 再次使用平方公式（a+b）(a-b)=a^2 -b^2
= -[(x^2+y^2-z^2)^2-4x^2y^2]
= -[( x^2+y^2)^2+Z^4-2Z^2X^2-2Z^2Y^2-4x^2y^2]
= -(x^4+y^4 + Z^4- -2Z^2X^2-2Z^2Y^2-2x^2y^2 )
= 2Z^2X^2+2Z^2Y^2+2x^2y^2 -x^4-y^4 +-Z^4
原式=[x^2-(y-z)^2]*[(y-z)^2-x^2]
=-[x^2-(y-z)^2]^2
=-x^4+2x^2(y-z)^2-(y-z)^4
（x+y+z)(-x+y+z)(x-y+z)(x+y-z)
=[(y+z)^2 -x^2][x^2-(y-z)^2]
= -x^4 +x^2*[2y^2+2z^2] - (y^2-z^2)^2
=-x^4-y^4-z^4 +2x^2*y^2 +2x^2*z^2 +2y^2*z^2
=2(x^2*y^2 +x^2*z^2 +y^2*z^2)-(x^4+y^4+z^4)
好了~求采纳！/(ㄒoㄒ)/~~
原式=[x^2-(y-z)^2]*[(y-z)^2-x^2]
=-[x^2-(y-z)^2]^2
=-x^4+2x^2(y-z)^2-(y-z)^4
（x+y+z)(-x+y+z)(x-y+z)(x+y-z)
=[(x+y+z)(x+y-z)]*{[z+(x-y)][z-(x-y)]}
=[(x+y)^2-z^2][z^2-(x-y)^2]
=(x^2+2xy+y^2-z^2)[z^2-(x-y)^2]
=4*x^2*y^2-(x^2+y^2-z^2)^2
不懂的欢迎追问，如有帮助请采纳，谢谢!