`(69842xx69842-30158xx30158)/(69842-30158)=?`

Options

A. 100000
B. 69842
C. 39684
D. 30158

Answer

To solve the expression \((69842 \times 69842 - 30158 \times 30158) / (69842 - 30158)\), 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 \(A = 69842\)
- Let \(B = 30158\)

2. **Apply the Difference of Squares Formula**:
- The expression can be rewritten as:
\[ \frac{A^2 - B^2}{A - B} \]
- Using the formula, we can express \(A^2 - B^2\) as:
\[ (A + B)(A - B) \]

3. **Substitute into the Expression**:
- Substitute \(A + B\) and \(A - B\):
\[ \frac{(A + B)(A - B)}{A - B} \]

4. **Cancel Out \(A - B\)**:
- Since \(A - B\) is in both the numerator and the denominator, we can cancel it out:
\[ A + B \]

5. **Calculate \(A + B\)**:
- Now, we need to calculate \(A + B\):
\[ A + B = 69842 + 30158 \]

6. **Perform the Addition**:
- Adding the two numbers:
\[ 69842 + 30158 = 100000 \]

7. **Final Answer**:
- Therefore, the result of the expression is:
\[ 100000 \]