Evaluate using suitable identitiie.
`18 1 ^(2) - 19^(2)`

Answer

To evaluate the expression \( 181^2 - 19^2 \) using suitable identities, we can apply the difference of squares identity, which states:

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

### Step-by-Step Solution:

1. **Identify \( a \) and \( b \)**:
- Here, \( a = 181 \) and \( b = 19 \).

2. **Apply the difference of squares identity**:
- Substitute \( a \) and \( b \) into the identity:
\[ 181^2 - 19^2 = (181 - 19)(181 + 19) \]

3. **Calculate \( 181 - 19 \)**:
- Perform the subtraction:
\[ 181 - 19 = 162 \]

4. **Calculate \( 181 + 19 \)**:
- Perform the addition:
\[ 181 + 19 = 200 \]

5. **Multiply the results from steps 3 and 4**:
- Now, multiply \( 162 \) and \( 200 \):
\[ 162 \times 200 \]

6. **Break down the multiplication**:
- We can simplify this multiplication:
\[ 162 \times 200 = 162 \times (2 \times 100) = (162 \times 2) \times 100 \]
- Calculate \( 162 \times 2 \):
\[ 162 \times 2 = 324 \]
- Now multiply by \( 100 \):
\[ 324 \times 100 = 32400 \]

7. **Final Answer**:
- Thus, the value of \( 181^2 - 19^2 \) is:
\[ \boxed{32400} \]