2. Simplify completely. \( \left(-a^{2}-5 a+3\right)-\left(a^{2}+3 a-2\right) \)

To simplify the expression \(\left(-a^{2}-5 a+3\right)-\left(a^{2}+3 a-2\right)\), start by distributing the negative sign across the second set of parentheses: \[ -a^{2} - 5a + 3 - a^{2} - 3a + 2 \] Now, combine like terms: \[ (-a^{2} - a^{2}) + (-5a - 3a) + (3 + 2) = -2a^{2} - 8a + 5 \] So the completely simplified expression is: \[ -2a^{2} - 8a + 5 \]