2) \( \begin{array}{l}10-2(-1+2:-2)+2^{2} \\ 10-2(-1-1)+2^{2}-5 \\ 10-2(-2)+2^{2}-5\end{array} \)

Let's break down the expression step by step: 1. The original expression is: \[ 10 - 2(-1 + 2 : -2) + 2^{2} \] 2. First, we simplify what's inside the parentheses. The operation \(2 : -2\) is division, which gives: \[ 2 : -2 = -1 \] Substituting that back, we have: \[ 10 - 2(-1 - 1) + 2^{2} \] 3. Now, simplify inside the parentheses: \[ -1 - 1 = -2 \] Now substituting gives us: \[ 10 - 2(-2) + 2^{2} \] 4. Next step is to simplify \(2^{2}\): \[ 2^{2} = 4 \] Now the expression looks like: \[ 10 - 2(-2) + 4 \] 5. Now, calculate \(2(-2)\): \[ 2(-2) = -4 \] So we substitute that in: \[ 10 - (-4) + 4 \] 6. When you subtract a negative number, it’s like adding: \[ 10 + 4 + 4 \] 7. Adding these numbers gives: \[ 10 + 4 = 14 \quad \text{and then} \quad 14 + 4 = 18 \] Thus, the final simplified result of the entire expression is: \[ \boxed{18} \]