(b) \( \left(-x^{2}+6 x-2\right)-\left(2 x^{2}+9 x-7\right) \)

To simplify the expression, start by distributing the negative sign across the second set of parentheses: \[ -x^{2} + 6x - 2 - 2x^{2} - 9x + 7 \] Now, combine like terms: 1. For the \(x^{2}\) terms: \(-x^{2} - 2x^{2} = -3x^{2}\) 2. For the \(x\) terms: \(6x - 9x = -3x\) 3. For the constant terms: \(-2 + 7 = 5\) Putting it all together, the simplified expression is: \[ -3x^{2} - 3x + 5 \]