find the value of `(108)^(2)`

Answer

To find the value of \( (108)^2 \), we can use the formula for the square of a binomial. We can express \( 108 \) as \( 110 - 2 \).

### Step-by-step Solution:

1. **Express 108 in terms of a binomial**:
\[ 108 = 110 - 2 \]

2. **Apply the formula for the square of a binomial**:
\[ (a - b)^2 = a^2 - 2ab + b^2 \]
Here, \( a = 110 \) and \( b = 2 \).

3. **Calculate \( a^2 \)**:
\[ a^2 = (110)^2 = 12100 \]

4. **Calculate \( b^2 \)**:
\[ b^2 = (2)^2 = 4 \]

5. **Calculate \( 2ab \)**:
\[ 2ab = 2 \times 110 \times 2 = 440 \]

6. **Combine all parts**:
\[ (110 - 2)^2 = 110^2 - 2 \cdot 110 \cdot 2 + 2^2 \]
\[ = 12100 - 440 + 4 \]

7. **Perform the subtraction and addition**:
\[ 12100 - 440 = 11660 \]
\[ 11660 + 4 = 11664 \]

8. **Final result**:
\[ (108)^2 = 11664 \]