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.

Learn how to solve the arithmetic expression (-25 - (-20) - 1) - (1 - 4 - 1) step-by-step. This problem covers arithmetic operations with negative numbers and order of operations. Suitable for students in Grades 6-8.

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