Evaluate
`{(405)^(2) - (395)^(2)}.`

Answer

To evaluate \( 405^2 - 395^2 \), we can use the difference of squares formula, which states that:

\[ A^2 - B^2 = (A - B)(A + B) \]

### Step-by-Step Solution:

1. **Identify A and B**:
- Here, we can let \( A = 405 \) and \( B = 395 \).

2. **Apply the Difference of Squares Formula**:
- Substitute \( A \) and \( B \) into the formula:
\[ 405^2 - 395^2 = (405 - 395)(405 + 395) \]

3. **Calculate \( A - B \)**:
- Calculate \( 405 - 395 \):
\[ 405 - 395 = 10 \]

4. **Calculate \( A + B \)**:
- Calculate \( 405 + 395 \):
\[ 405 + 395 = 800 \]

5. **Multiply the Results**:
- Now, multiply the two results:
\[ 10 \times 800 = 8000 \]

### Final Answer:
Thus, \( 405^2 - 395^2 = 8000 \).

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