`(63)^(2)-(12)^(2)=?`

Options

A. 3528
B. 3852
C. 3582
D. 3825

Explanation

To solve the expression \( (63)^2 - (12)^2 \), we can use the difference of squares formula. The difference of squares states that:

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

In this case, let \( a = 63 \) and \( b = 12 \).

### Step 1: Identify \( a \) and \( b \)
We have:
- \( a = 63 \)
- \( b = 12 \)

### Step 2: Apply the difference of squares formula
Using the formula, we can rewrite the expression as:

\[ (63)^2 - (12)^2 = (63 - 12)(63 + 12) \]

### Step 3: Calculate \( 63 - 12 \) and \( 63 + 12 \)
Now, we calculate the two parts:
- \( 63 - 12 = 51 \)
- \( 63 + 12 = 75 \)

### Step 4: Multiply the results
Now, we multiply the results from the previous step:

\[ (63)^2 - (12)^2 = 51 \times 75 \]

### Step 5: Calculate \( 51 \times 75 \)
To calculate \( 51 \times 75 \), we can break it down:

\[ 51 \times 75 = 51 \times (70 + 5) = 51 \times 70 + 51 \times 5 \]

Calculating each part:
- \( 51 \times 70 = 3570 \)
- \( 51 \times 5 = 255 \)

Now, add these two results together:

\[ 3570 + 255 = 3825 \]

### Final Answer
Thus, the value of \( (63)^2 - (12)^2 \) is:

\[ \boxed{3825} \]