\[3x(3x + 7) - (3x + 1)^{2} =\]
\[= 9x^{2} + 21x - \left( 9x^{2} + 6x + 1 \right) =\]
\[= 9x^{2} + 21x - 9x^{2} - 6x - 1 =\]
\[= 15x - 1.\]