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

Options

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

Answer

To solve the expression \( 249^2 - 248^2 \), we can use the difference of squares formula, which states that:

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

Here, we can let \( a = 249 \) and \( b = 248 \).

### Step 1: Identify \( a \) and \( b \)
We have:
- \( a = 249 \)
- \( b = 248 \)

### Step 2: Apply the difference of squares formula
Using the formula, we can rewrite the expression as:

\[ 249^2 - 248^2 = (249 - 248)(249 + 248) \]

### Step 3: Calculate \( 249 - 248 \)
Now, we calculate \( 249 - 248 \):

\[ 249 - 248 = 1 \]

### Step 4: Calculate \( 249 + 248 \)
Next, we calculate \( 249 + 248 \):

\[ 249 + 248 = 497 \]

### Step 5: Multiply the results
Now we multiply the two results together:

\[ (249 - 248)(249 + 248) = 1 \times 497 = 497 \]

### Final Answer
Thus, the value of \( 249^2 - 248^2 \) is:

\[ \boxed{497} \]