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

\[
(4 - 5)^2 (8 \times 2 + 3)^2
\]

### Step 1: Simplify each part.

#### First term: \( (4 - 5)^2 \)
\[
4 - 5 = -1 \quad \text{so} \quad (-1)^2 = 1
\]

#### Second term: \( (8 \times 2 + 3)^2 \)
\[
8 \times 2 = 16 \quad \text{and} \quad 16 + 3 = 19 \quad \text{so} \quad 19^2 = 361
\]

### Step 2: Multiply the simplified results.
\[
1 \times 361 = 361
\]

Thus, the final value of the expression is:
\[
\boxed{361}
\]

Would you like more details or have any questions?

Here are 5 questions related to this problem:
1. What happens when we square a negative number?
2. How does the order of operations (PEMDAS) apply to this expression?
3. Can you try another similar expression, like \( (3 - 7)^2 (5 \times 2 + 1)^2 \)?
4. How do squares of binomials differ from squaring single terms?
5. How would the result change if the powers were different (e.g., cubes)?

**Tip:** Always simplify the terms inside parentheses before applying exponents or multiplication.

Learn how to simplify and solve the expression (4 - 5)² (8 × 2 + 3)² by following the correct order of operations (PEMDAS). This problem covers key algebraic concepts, including exponentiation and simplifying terms in parentheses. Suitable for students in Grades 8-10.

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