Evaluate
`{(7.8)^(2) - (2.2)^(2)}.`

Answer

To evaluate the expression \( (7.8)^2 - (2.2)^2 \), we can use the difference of squares formula, which states that:

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

### Step-by-Step Solution:

1. **Identify A and B**:
Here, we can let \( A = 7.8 \) and \( B = 2.2 \).

2. **Apply the Difference of Squares Formula**:
Using the formula, we can rewrite the expression:
\[ (7.8)^2 - (2.2)^2 = (7.8 + 2.2)(7.8 - 2.2) \]

3. **Calculate \( A + B \)**:
Now, calculate \( 7.8 + 2.2 \):
\[ 7.8 + 2.2 = 10 \]

4. **Calculate \( A - B \)**:
Next, calculate \( 7.8 - 2.2 \):
\[ 7.8 - 2.2 = 5.6 \]

5. **Multiply the Results**:
Now, substitute back into the equation:
\[ (7.8)^2 - (2.2)^2 = (10)(5.6) \]
Now, calculate \( 10 \times 5.6 \):
\[ 10 \times 5.6 = 56 \]

6. **Final Answer**:
Therefore, the value of \( (7.8)^2 - (2.2)^2 \) is:
\[ \boxed{56} \]