\( - 2 - [ 4 - ( - 1 - 2 ( 2 ) ^ { 2 } - 20 = ( - 2 ) + ( - 1 ) + 2 ^ { 2 } \)

Let's simplify the expression step by step. The expression you provided seems to have some formatting issues, but I will interpret it as follows: \[ -2 - [4 - (-1 - 2(2)^2 - 20)] = (-2) + (-1) + 2^2 \] First, let's simplify the left side of the equation: 1. Calculate \(2^2\): \[ 2^2 = 4 \] 2. Substitute \(2^2\) into the expression: \[ -2 - [4 - (-1 - 2(4) - 20)] \] 3. Calculate \(2(4)\): \[ 2(4) = 8 \] 4. Substitute \(8\) into the expression: \[ -2 - [4 - (-1 - 8 - 20)] \] 5. Combine the terms inside the parentheses: \[ -1 - 8 - 20 = -29 \] 6. Substitute \(-29\) into the expression: \[ -2 - [4 - (-29)] \] 7. Simplify \(4 - (-29)\): \[ 4 + 29 = 33 \] 8. Substitute \(33\) into the expression: \[ -2 - 33 \] 9. Finally, calculate \(-2 - 33\): \[ -2 - 33 = -35 \] Now, let's simplify the right side of the equation: 1. Substitute \(2^2\) into the expression: \[ (-2) + (-1) + 4 \] 2. Combine the terms: \[ -2 - 1 + 4 = -3 + 4 = 1 \] Now we have: Left side: \(-35\) Right side: \(1\) Thus, the equation simplifies to: \[ -35 \neq 1 \] Therefore, the original equation does not hold true. If you have a different interpretation or need further assistance, please let me know!