Calculate the value of `((59881 times 59881-49681 times 49681))/(10200)`

Options

A. 110956
B. 109562
C. 109652
D. 109662

Answer

To solve the expression \(\frac{(59881 \times 59881 - 49681 \times 49681)}{10200}\), 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 \(b\)**:
- Let \(a = 59881\) and \(b = 49681\).

2. **Apply the difference of squares formula**:
- We can rewrite the expression as:
\[ a^2 - b^2 = (a - b)(a + b) \]

3. **Calculate \(a - b\)**:
- \(a - b = 59881 - 49681 = 10200\)

4. **Calculate \(a + b\)**:
- \(a + b = 59881 + 49681 = 109562\)

5. **Substitute back into the formula**:
- Now we can substitute \(a - b\) and \(a + b\) back into the formula:
\[ a^2 - b^2 = (10200)(109562) \]

6. **Set up the full expression**:
- The expression now becomes:
\[ \frac{(10200)(109562)}{10200} \]

7. **Cancel out \(10200\)**:
- The \(10200\) in the numerator and denominator cancels out:
\[ 109562 \]

8. **Final Result**:
- Therefore, the final value is:
\[ 109562 \]