已知z2=x2+y2,化简(x+y+z)(x-y+z)(-x+y+z)(x+y-z).

问题描述:

已知z2=x2+y2,化简(x+y+z)(x-y+z)(-x+y+z)(x+y-z).

原式=(x+y+z)(x+y-z)(x-y+z)(-x+y+z)
=[(x+y)2-z2][z2-(x-y)2]
=(x2+y2+2xy-z2)(z2-x2-y2+2xy)
把z2=x2+y2代入得,
原式=2xy•2xy=4x2y2