Evaluate `{(83)^(2) - (17)^(2)}`.

Answer

To evaluate \( (83)^2 - (17)^2 \), we can use the difference of squares formula, which states that:

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

In this case, let \( A = 83 \) and \( B = 17 \).

### Step 1: Identify A and B
We have:
- \( A = 83 \)
- \( B = 17 \)

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

\[ (83)^2 - (17)^2 = (83 + 17)(83 - 17) \]

### Step 3: Calculate \( A + B \) and \( A - B \)
Now, we calculate \( A + B \) and \( A - B \):

\[ A + B = 83 + 17 = 100 \]
\[ A - B = 83 - 17 = 66 \]

### Step 4: Substitute back into the expression
Now we substitute these values back into the expression:

\[ (83)^2 - (17)^2 = (100)(66) \]

### Step 5: Calculate the final result
Now, we multiply \( 100 \) and \( 66 \):

\[ 100 \times 66 = 6600 \]

Thus, the final answer is:

\[ (83)^2 - (17)^2 = 6600 \]