(x+y-z)(x-y+z)-(y+z-x)(z-x-y)
=[x+(y-z)][x-(y-z)]-[(z-x)+y][(z-x)-y]
=x^2-(y-z)^2-[(z-x)^2-y^2]
=x^2-(z-x)^2+y^2-(y-z)^2
=(x+z-x)(x-z+x)+(y+y-z)(y-y+z)
=z(2x-z)+(2y-z)z
=z(2x-z+2y-z)
=2z(x+y-z)
(x+y-z)(x-y+z)-(y+z-x)(z-x-y)
=[x+(y-z)][x-(y-z)]-[(z-x)+y][(z-x)-y]
=x^2-(y-z)^2-[(z-x)^2-y^2]
=x^2-(z-x)^2+y^2-(y-z)^2
=(x+z-x)(x-z+x)+(y+y-z)(y-y+z)
=z(2x-z)+(2y-z)z
=z(2x-z+2y-z)
=2z(x+y-z)