\[(x - y - 3)(x - y + 3) =\]
\[= \left( (x - y) - 3 \right)\left( (x - y) + 3 \right) =\]
\[= (x - y)^{2} - 3^{2} =\]
\[= x^{2} - 2xy + y^{2} - 9.\]