Find ` (2x+3y)^2`

Answer

To find \( (2x + 3y)^2 \), we can use the formula for the square of a binomial, which is given by:

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

### Step-by-step Solution:

1. **Identify \( a \) and \( b \)**:
- Here, \( a = 2x \) and \( b = 3y \).

2. **Apply the formula**:
- Substitute \( a \) and \( b \) into the formula:
\[ (2x + 3y)^2 = (2x)^2 + (3y)^2 + 2(2x)(3y) \]

3. **Calculate \( (2x)^2 \)**:
- \( (2x)^2 = 4x^2 \)

4. **Calculate \( (3y)^2 \)**:
- \( (3y)^2 = 9y^2 \)

5. **Calculate \( 2(2x)(3y) \)**:
- \( 2(2x)(3y) = 12xy \)

6. **Combine all the terms**:
- Now, combine the results from steps 3, 4, and 5:
\[ (2x + 3y)^2 = 4x^2 + 9y^2 + 12xy \]

### Final Answer:
\[ (2x + 3y)^2 = 4x^2 + 9y^2 + 12xy \]