`(18.43 xx 18.43 - 6.57 xx 6.57)/(11.86) = ?`

Options

A. 32.62
B. 25
C. 26
D. 24.12

Answer

To solve the expression \((18.43 \times 18.43 - 6.57 \times 6.57) / 11.86\), we can follow these steps:

### Step 1: Identify the expression
We start with the expression:
\[ \frac{(18.43 \times 18.43) - (6.57 \times 6.57)}{11.86} \]

### Step 2: Recognize the squares
We can rewrite the expression using squares:
\[ \frac{(18.43^2 - 6.57^2)}{11.86} \]

### Step 3: Apply the difference of squares formula
We can use the difference of squares formula, which states that \(a^2 - b^2 = (a + b)(a - b)\). Here, \(a = 18.43\) and \(b = 6.57\):
\[ = \frac{(18.43 + 6.57)(18.43 - 6.57)}{11.86} \]

### Step 4: Calculate \(a + b\) and \(a - b\)
Now we calculate \(a + b\) and \(a - b\):
- \(a + b = 18.43 + 6.57 = 25\)
- \(a - b = 18.43 - 6.57 = 11.86\)

### Step 5: Substitute back into the expression
Now substitute these values back into the expression:
\[ = \frac{(25)(11.86)}{11.86} \]

### Step 6: Simplify the expression
Now, we can simplify the expression:
\[ = 25 \]

### Final Answer
Thus, the value of the expression is:
\[ \boxed{25} \]