Evaluate: `(a+2b)^(2)`

Answer

To evaluate \((a + 2b)^{2}\), we can use the formula for the square of a binomial, which states:

\[ (x + y)^{2} = x^{2} + y^{2} + 2xy \]

### Step-by-Step Solution:

1. **Identify \(x\) and \(y\)**:
- Here, let \(x = a\) and \(y = 2b\).

2. **Apply the formula**:
- Substitute \(x\) and \(y\) into the formula:
\[ (a + 2b)^{2} = a^{2} + (2b)^{2} + 2 \cdot a \cdot (2b) \]

3. **Calculate \( (2b)^{2} \)**:
- Calculate \( (2b)^{2} \):
\[ (2b)^{2} = 4b^{2} \]

4. **Calculate \( 2 \cdot a \cdot (2b) \)**:
- Calculate \( 2 \cdot a \cdot (2b) \):
\[ 2 \cdot a \cdot (2b) = 4ab \]

5. **Combine all parts**:
- Now, combine all the parts together:
\[ (a + 2b)^{2} = a^{2} + 4b^{2} + 4ab \]

### Final Answer:
\[ (a + 2b)^{2} = a^{2} + 4ab + 4b^{2} \]