Question

如何化简(x+y+z)(x+y-z)(x-y+z)(-x+y+z)

Answer 1

应用平方差公式
a^2-b^2=(a+b)(a-b)
(x+y+z)(x+y-z)(x-y+z)(-x+y+z)
=[(x+y)^2-z^2][z^2-(x-y)^2]
=-z^4+[(x+y)^2+(x-y)^2]z^2-(x+y)^2(x-y)^2
=-z^4+2(x^2+y^2)z^2-(x^2-y^2)^2

这算是化简了

Answer 2

-x^4 + 2 x^2 y^2 - y^4 + 2 x^2 z^2 + 2 y^2 z^2 - z^4
或着-x^4 - (y^2 - z^2)^2 + 2 x^2 (y^2 + z^2)

Answer 3

学过这个公式么？(a+b)*(a-b)=a平方-b平方
前面两个把x+y当整体
最后一个提出个负号，然后就是后面两个把x-y当整体
再套公式应该很容易了

Answer 4

(X+Y-Z)+(-X+Y-Z)
=X+Y-Z-X+Y-Z
=2Y-2Z
=2(Y-Z)

Answer 5

=x+y-z-x+y-z
=2y-2z

Answer 6

不懂了