`(32.51)^(2)-(17.45)^(2)=?`

Options

A. 780
B. 850
C. 680
D. 750

Explanation

To solve the equation \( (32.51)^2 - (17.45)^2 \), we can use the difference of squares formula, which states that:

\[ A^2 - B^2 = (A - B)(A + B) \]

### Step 1: Round the Numbers
First, we round the numbers to make calculations easier.
- Round \( 32.51 \) to \( 32 \)
- Round \( 17.45 \) to \( 17 \)

### Step 2: Identify A and B
Now we identify:
- \( A = 32 \)
- \( B = 17 \)

### Step 3: Apply the Difference of Squares Formula
Using the difference of squares formula:

\[ (32)^2 - (17)^2 = (32 - 17)(32 + 17) \]

### Step 4: Calculate A - B and A + B
Now, we calculate:
- \( A - B = 32 - 17 = 15 \)
- \( A + B = 32 + 17 = 49 \)

### Step 5: Multiply the Results
Now we multiply the results from the previous step:

\[ (32 - 17)(32 + 17) = 15 \times 49 \]

### Step 6: Calculate 15 x 49
Now we can calculate \( 15 \times 49 \):

\[ 15 \times 49 = 735 \]

### Final Answer
Thus, the value of \( (32.51)^2 - (17.45)^2 \) is approximately \( 735 \).

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