Simplify. \[ \left(-5 v^{2}+7 v-2\right)-\left(-2 v^{2}-2 v+7\right)+\left(6 v^{2}-7 v+4\right) \] \( \square \)

To simplify the expression, we start by distributing the negative sign through the second set of parentheses: \[ \left(-5 v^{2} + 7 v - 2\right) + \left(2 v^{2} + 2 v - 7\right) + \left(6 v^{2} - 7 v + 4\right) \] Next, we can combine like terms. We will group the \(v^2\) terms, the \(v\) terms, and the constant terms separately: 1. \(v^2\) terms: \[ -5 v^2 + 2 v^2 + 6 v^2 = (6 - 5 + 2)v^2 = 3 v^2 \] 2. \(v\) terms: \[ 7 v + 2 v - 7 v = (7 + 2 - 7)v = 2 v \] 3. Constant terms: \[ -2 - 7 + 4 = (-2 - 7 + 4) = -5 \] Now we combine all the simplified terms together: \[ 3v^2 + 2v - 5 \] Thus, the simplified expression is \[ \boxed{3v^2 + 2v - 5} \]