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：369 ℃　时间：2020-09-25 13:44:02

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)*...