1. Factorize $(x y-1)^{2}+(x+y-2)(x+y$ $-2 x y)$.
Let $x y=a, x+y=b$, so

the original expression $\mathrm{x}^{2}=(a-1)^{2}+(b-2)(0-2 a)=(a-b+1)^{2}$.
Substituting into the
resulting expression $=(x-1)^{2}(y-1)^{2}$.