To solve the expression $(-25 - (-20) - 1) - (1 - 4 - 1)$, let's evaluate it step-by-step.

Step 1: Simplify each part of the expression inside the parentheses.

1. First Parentheses: $-25 - (-20) - 1$

$-25 - (-20) - 1 = -25 + 20 - 1$

Simplifying further:

$-25 + 20 = -5$

$-5 - 1 = -6$

So, the first part simplifies to $-6$.

2. Second Parentheses: $1 - 4 - 1$

$1 - 4 - 1$

Simplifying from left to right:

$1 - 4 = -3$

$-3 - 1 = -4$

So, the second part simplifies to $-4$.

Step 2: Combine the simplified parts.

Now, subtract the second part from the first part:

$-6 - (-4)$

Since subtracting a negative is the same as adding a positive:

$-6 + 4$

$-6 + 4 = -2$

Final Answer:

$\boxed{-2}$

Would you like a more detailed explanation, or do you have any other questions?

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Here are 5 related questions that expand on this concept:

1. How would the result change if the expression was $(-25 - (-20) - 1) + (1 - 4 - 1)$?
2. What is the result of $(-30 - (-15) - 5) - (2 - 3 - 4)$?
3. Can you simplify $(a - (-b) - c) - (x - y - z)$ for general $a, b, c, x, y,$ and $z$?
4. How does changing the order of operations affect the outcome in expressions with multiple subtractions?
5. What happens to the result if all numbers in the expression are positive?

Tip: When working with negative signs, remember that subtracting a negative number is equivalent to adding the absolute value of that number.