`(92)^(2)`

Answer

To find the square of \( 92 \), we can use the algebraic identity for the square of a binomial, which states that:

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

### Step-by-Step Solution:

1. **Identify \( a \) and \( b \)**:
Let's express \( 92 \) as \( (90 + 2) \). Here, \( a = 90 \) and \( b = 2 \).

2. **Apply the identity**:
Using the identity, we can write:
\[ (90 + 2)^2 = 90^2 + 2 \cdot 90 \cdot 2 + 2^2 \]

3. **Calculate \( a^2 \)**:
First, calculate \( 90^2 \):
\[ 90^2 = 8100 \]

4. **Calculate \( 2ab \)**:
Next, calculate \( 2 \cdot 90 \cdot 2 \):
\[ 2 \cdot 90 \cdot 2 = 360 \]

5. **Calculate \( b^2 \)**:
Now, calculate \( 2^2 \):
\[ 2^2 = 4 \]

6. **Combine all the parts**:
Now we can combine all the calculated parts:
\[ (90 + 2)^2 = 90^2 + 2 \cdot 90 \cdot 2 + 2^2 = 8100 + 360 + 4 \]

7. **Final calculation**:
Adding these together gives:
\[ 8100 + 360 + 4 = 8464 \]

Thus, the square of \( 92 \) is \( 8464 \).