\[81x^{2} - (9x + 7y)^{2} =\]
\[= 81x^{2} - \left( (9x)^{2} + 2 \cdot 9x \cdot 7y + (7y)^{2} \right) =\]
\[= 81x^{2} - 81x^{2} - 126xy - 49y^{2} =\]
\[= - 49y^{2} - 126xy\text{.\ }\]