题目

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

提问时间：2021-03-14

答案

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)*...