Evaluate using suitable identitiie.
`(48) ^(2)`

Answer

To evaluate \( (48)^2 \) using suitable identities, we can use the identity for the square of a binomial, specifically \( (a - b)^2 = a^2 - 2ab + b^2 \).

### Step-by-Step Solution:

1. **Rewrite 48 in terms of a nearby round number**:
We can express 48 as \( 50 - 2 \).

\[ (48)^2 = (50 - 2)^2 \]

2. **Apply the binomial square identity**:
Using the identity \( (a - b)^2 = a^2 - 2ab + b^2 \), we set \( a = 50 \) and \( b = 2 \).

\[ (50 - 2)^2 = 50^2 - 2 \cdot 50 \cdot 2 + 2^2 \]

3. **Calculate each term**:
- Calculate \( 50^2 \):

\[ 50^2 = 2500 \]

- Calculate \( 2^2 \):

\[ 2^2 = 4 \]

- Calculate \( 2 \cdot 50 \cdot 2 \):

\[ 2 \cdot 50 \cdot 2 = 200 \]

4. **Combine the results**:
Substitute these values back into the expression:

\[ (50 - 2)^2 = 2500 - 200 + 4 \]

Now perform the arithmetic:

\[ 2500 - 200 = 2300 \]
\[ 2300 + 4 = 2304 \]

5. **Final result**:
Therefore,

\[ (48)^2 = 2304 \]