化简 (x+y+z)^2-(-x+y+z)^ 2+(x-y+z)^ 2-(x+y-z)^ 2_数学解答

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

人气：456 ℃　时间：2020-09-25 16:19:27

解答

利用A^2-B^2=(A+B)(A-B)即可.
(x+y+z)^2-(-x+y+z)^2+(x-y+z)^2-(x+y-z)^2
=[(x+y+z)^2-(-x+y+z)^2]+[(x-y+z)^2-(x+y-z)^2]
={[(x+y+z)+(-x+y+z)]*[(x+y+z)-(-x+y+z)]}+{[(x-y+z)+(x+y-z)]*[(x-y+z)-(x+y-z)]}
=[(2y+2z)*2x]+[2x*(-2y)]
=4xy+4xz+(-4xy)
=4xz