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 algebraic identity that states:

\[ a^2 - b^2 = (a + b)(a - b) \]

### Step 1: Identify \(a\) and \(b\)
Let:
- \(a = 525 + 252\)
- \(b = 525 - 252\)

### Step 2: Apply the identity
Using the identity, we can rewrite the expression as:

\[ (525 + 252)^2 - (525 - 252)^2 = [(525 + 252) + (525 - 252)][(525 + 252) - (525 - 252)] \]

### Step 3: Simplify the terms
Calculating the terms:
- \((525 + 252) + (525 - 252) = 525 + 252 + 525 - 252 = 2 \times 525 = 1050\)
- \((525 + 252) - (525 - 252) = 525 + 252 - 525 + 252 = 2 \times 252 = 504\)

### Step 4: Substitute back into the expression
Now substituting back, we have:

\[ (525 + 252)^2 - (525 - 252)^2 = 1050 \times 504 \]

### Step 5: Substitute into the original expression
Now, substituting this back into the original expression gives us:

\[ \frac{1050 \times 504}{525 \times 252} \]

### Step 6: Simplify the fraction
We can simplify this expression. Notice that:

\[ 1050 = 2 \times 525 \quad \text{and} \quad 504 = 2 \times 252 \]

Thus, we can rewrite it as:

\[ \frac{(2 \times 525) \times (2 \times 252)}{525 \times 252} = \frac{4 \times 525 \times 252}{525 \times 252} \]

### Step 7: Cancel out the common terms
The \(525 \times 252\) in the numerator and denominator cancels out:

\[ = 4 \]

### Final Answer
Thus, the value of the expression is \(4\).