\(\begin{array}{l}
a){\rm{ }}\left( {{\rm{ }}x + 1} \right)\left( {x + 3} \right) - \left( {x - 1} \right)\left( {x - 3} \right) + {\rm{ }}2x\left( {1 - x} \right)\\
= {x^2} + 3x + x + 3 - \left( {{x^2} - 3x - x + 3} \right) + 2x - 2{x^2}\\
= {x^2} + 4x + 3 - {x^2} + 3x + x - 3 + 2x - 2{x^2}\\
= - 2{x^2} + 10x\\
b){\rm{ }}\left( {3x{\rm{ }} + 1} \right)\left( {x + 1} \right){\rm{ }} - {\rm{ }}\left( {x + 3} \right)\left( {3x - 2} \right)\\
= 3{x^2} + 3x + x + 1 - \left( {3{x^2} - 2x + 9x - 6} \right)\\
= 3{x^2} + 4x + 1 - 3{x^2} + 2x - 9x + 6\\
= - 3x + 7
\end{array}\)