Find the value of `[(525 +252)^(2)-(525 -252)^(2)]//(525 xx 252)` .
A. 3
B. 4
C. 5
D. 6

Options

A. C
B. A
C. B
D. D

Answer

To solve the expression \(\frac{(525 + 252)^2 - (525 - 252)^2}{525 \times 252}\), we can use the difference of squares formula.

### Step-by-step Solution:

1. **Identify the expression**:
We start with the expression:
\[ \frac{(525 + 252)^2 - (525 - 252)^2}{525 \times 252} \]

2. **Apply the difference of squares formula**:
Recall that \(a^2 - b^2 = (a - b)(a + b)\). Here, let:
- \(a = 525 + 252\)
- \(b = 525 - 252\)

Thus, we can rewrite the expression:
\[ (525 + 252)^2 - (525 - 252)^2 = [(525 + 252) - (525 - 252)][(525 + 252) + (525 - 252)] \]

3. **Simplify the terms**:
- The first term simplifies to:
\[ (525 + 252) - (525 - 252) = 525 + 252 - 525 + 252 = 2 \times 252 = 504 \]
- The second term simplifies to:
\[ (525 + 252) + (525 - 252) = 525 + 252 + 525 - 252 = 2 \times 525 = 1050 \]

4. **Combine the results**:
Now we have:
\[ (525 + 252)^2 - (525 - 252)^2 = 504 \times 1050 \]

5. **Substitute back into the expression**:
Substitute this back into our original expression:
\[ \frac{504 \times 1050}{525 \times 252} \]

6. **Simplify the fraction**:
Notice that \(504\) can be expressed as \(2 \times 252\):
\[ \frac{(2 \times 252) \times 1050}{525 \times 252} \]
Cancel \(252\) from numerator and denominator:
\[ \frac{2 \times 1050}{525} \]

7. **Further simplify**:
Now, we can simplify \( \frac{1050}{525} = 2\):
\[ 2 \times 2 = 4 \]

8. **Final answer**:
Thus, the value of the expression is:
\[ \boxed{4} \]