Let's break down and simplify the given expression step by step:

The expression is:

\[
-45^2 - \left( -45(-4) - (-4) \right)
\]

### Step 1: Simplify \( -45^2 \)
- When squaring a number, remember that squaring a negative number results in a positive value:
\[
-45^2 = -(45 \times 45) = -2025
\]

### Step 2: Simplify the terms inside the parentheses
#### \( -45(-4) \)
Multiplying \(-45\) by \(-4\) gives:
\[
-45 \times -4 = 180
\]

Now, let's move to the entire expression inside the parentheses:

\[
180 - (-4)
\]
Subtracting \(-4\) is equivalent to adding \(4\):
\[
180 + 4 = 184
\]

### Step 3: Substitute these values back into the original expression:
\[
-2025 - 184
\]
Now, simplify the subtraction:
\[
-2025 - 184 = -2209
\]

Thus, the final result of the expression is:

\[
\boxed{-2209}
\]

Would you like any further details or explanations?

Here are five related questions to extend your understanding:
1. How do you handle the negative sign when squaring a negative number?
2. Why does subtracting a negative number result in addition?
3. What is the effect of parentheses on mathematical operations?
4. How can you simplify complex expressions involving both multiplication and addition?
5. What are the properties of exponents with negative bases?

**Tip**: Always apply the order of operations (PEMDAS) carefully to avoid mistakes when dealing with expressions containing powers and parentheses.

Learn how to simplify the expression -45^2 -(-45(-4)-(-4)) step by step. This detailed solution covers key concepts such as exponents, handling negative numbers, and the order of operations (PEMDAS). Suitable for students in Grades 8-10.

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