Calculate the value of `((61681 xx61681 -31681 xx31681)/(30000))`

Options

A. 93352
B. 94362
C. 93362
D. 95362

Answer

To solve the expression \((61681 \times 61681 - 31681 \times 31681) / 30000\), we can use the difference of squares formula. Here's the step-by-step solution:

### Step 1: Identify A and B
Let:
- \( A = 61681 \)
- \( B = 31681 \)

### Step 2: Apply the Difference of Squares Formula
The difference of squares formula states that:
\[ A^2 - B^2 = (A - B)(A + B) \]
Thus, we can rewrite the expression as:
\[ \frac{A^2 - B^2}{30000} = \frac{(A - B)(A + B)}{30000} \]

### Step 3: Calculate \( A - B \)
Now, calculate \( A - B \):
\[ A - B = 61681 - 31681 = 30000 \]

### Step 4: Calculate \( A + B \)
Next, calculate \( A + B \):
\[ A + B = 61681 + 31681 = 93362 \]

### Step 5: Substitute Back into the Expression
Now substitute \( A - B \) and \( A + B \) back into the expression:
\[ \frac{(30000)(93362)}{30000} \]

### Step 6: Simplify the Expression
The \( 30000 \) in the numerator and denominator cancels out:
\[ 93362 \]

### Final Answer
Thus, the value of the expression is:
\[ \boxed{93362} \]