To simplify the polynomial expression \((xy - 2)(22 + 1)\), first simplify the expression inside the parentheses:
\[ 22 + 1 = 23 \]
Now, substitute this back into the expression:
\[ (xy - 2)(23) \]
Next, distribute 23 to both terms in the first polynomial:
\[ 23(xy) - 23(2) = 23xy - 46 \]
Thus, the simplified expression is:
\[ \boxed{23xy - 46} \]