the value of `249^(2)-248^(2)` is

Options

A. `1^(2)`
B. 477
C. 487
D. 497

Explanation

To solve the problem \( 249^2 - 248^2 \), we can use the algebraic identity for the difference of squares, which states:

\[ a^2 - b^2 = (a + b)(a - b) \]

### Step-by-Step Solution:

1. **Identify \( a \) and \( b \)**:
- Here, let \( a = 249 \) and \( b = 248 \).

2. **Apply the difference of squares formula**:
- Using the identity, we can rewrite the expression:
\[ 249^2 - 248^2 = (249 + 248)(249 - 248) \]

3. **Calculate \( 249 + 248 \)**:
- Adding the two numbers:
\[ 249 + 248 = 497 \]

4. **Calculate \( 249 - 248 \)**:
- Subtracting the two numbers:
\[ 249 - 248 = 1 \]

5. **Combine the results**:
- Now substitute back into the formula:
\[ 249^2 - 248^2 = 497 \times 1 \]

6. **Final calculation**:
- Therefore, the value is:
\[ 497 \times 1 = 497 \]

### Final Answer:
The value of \( 249^2 - 248^2 \) is \( 497 \).

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