To simplify the expression you've provided, we can break it down step by step:

1. **Expand each term**:
- \(2x(x - 4)^2\)
- \(-(x + 5)(x - 2)(x + 2)\)
- \(2(x + 5)^2\)
- \(-(x - 1)\)

2. **Combine and simplify**:
- Calculate each expanded term.
- Combine like terms.

Here are the calculations broken down:

### Step 1: Expand Each Term

1. **Expand \(2x(x - 4)^2\)**:
\[
(x - 4)^2 = x^2 - 8x + 16 \\
2x(x^2 - 8x + 16) = 2x^3 - 16x^2 + 32x
\]

2. **Expand \(-(x + 5)(x - 2)(x + 2)\)**:
- \( (x - 2)(x + 2) = x^2 - 4 \)
- \((x + 5)(x^2 - 4) = x^3 + 5x^2 - 4x - 20\)
- Negating gives us \(-x^3 - 5x^2 + 4x + 20\)

3. **Expand \(2(x + 5)^2\)**:
\[
(x + 5)^2 = x^2 + 10x + 25 \\
2(x^2 + 10x + 25) = 2x^2 + 20x + 50
\]

4. **Negate \(-(x - 1)\)**:
\(-x + 1\)

### Step 2: Combine All Expanded Terms

Combine all the expanded terms together:

\[
(2x^3 - 16x^2 + 32x) + (-x^3 - 5x^2 + 4x + 20) + (2x^2 + 20x + 50) + (-x + 1)
\]

### Step 3: Combine Like Terms

Combine all like terms:

- \(x^3\) terms: \(2x^3 - x^3 = x^3\)
- \(x^2\) terms: \(-16x^2 - 5x^2 + 2x^2 = -19x^2\)
- \(x\) terms: \(32x + 4x + 20x - x = 55x\)
- Constant terms: \(20 + 50 + 1 = 71\)

### Final Result

So, the simplified expression becomes:

\[
x^3 - 19x^2 + 55x + 71
\]

If you have further questions or need clarification on any specific step, feel free to ask!