已知z2=x2+y2,化简(x+y+z)(x-y+z)(-x+y+z)(x+y-z).
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已知z2=x2+y2,化简(x+y+z)(x-y+z)(-x+y+z)(x+y-z).
![已知z2=x2+y2,化简(x+y+z)(x-y+z)(-x+y+z)(x+y-z).](/uploads/image/z/16768086-6-6.jpg?t=%E5%B7%B2%E7%9F%A5z2%3Dx2%2By2%EF%BC%8C%E5%8C%96%E7%AE%80%EF%BC%88x%2By%2Bz%EF%BC%89%EF%BC%88x-y%2Bz%EF%BC%89%EF%BC%88-x%2By%2Bz%EF%BC%89%EF%BC%88x%2By-z%EF%BC%89%EF%BC%8E)
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.
=[(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.
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