By using an appropriate identity , find the following :
`(102)^(2)`

Answer

To find the value of \( (102)^2 \) using an appropriate identity, we can use the identity for the square of a binomial, which states:

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

### Step-by-Step Solution:

1. **Identify \( a \) and \( b \)**:
We can express \( 102 \) as \( 100 + 2 \). Here, we can take:
- \( a = 100 \)
- \( b = 2 \)

2. **Apply the identity**:
Using the identity \( (a + b)^2 = a^2 + 2ab + b^2 \), we substitute \( a \) and \( b \):
\[ (100 + 2)^2 = 100^2 + 2 \cdot 100 \cdot 2 + 2^2 \]

3. **Calculate \( a^2 \)**:
Calculate \( 100^2 \):
\[ 100^2 = 10000 \]

4. **Calculate \( 2ab \)**:
Calculate \( 2 \cdot 100 \cdot 2 \):
\[ 2 \cdot 100 \cdot 2 = 400 \]

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

6. **Combine all parts**:
Now, we add all the calculated parts together:
\[ 10000 + 400 + 4 = 10404 \]

Thus, the value of \( (102)^2 \) is \( 10404 \).