设xy=m,x+y=n
原式=(m-1)^2+(n-2m)(n-2)
=m^2-2m+1+n^2-(2+2m)n+4m
=(m-n)^2+2(m-n)
=(m-n)(m-n+2)
=(xy-x-y)(xy-x-y+2)t设x+y=t
原式=(xy-1)^2+(t-2xy)(t-2)
=(xy)^2-2xy+1+t^-2xyt-2t+4xy
=(xy-t)^2+2(xy-t)
=(xy-t)(xy-t+2)
=(xy-x-y)(xy-x-y+2)