Factorise :
`a^(2) - (2a + 3b)^(2)`

Answer

To factorise the expression \( a^2 - (2a + 3b)^2 \), we can use the difference of squares identity, which states that \( x^2 - y^2 = (x + y)(x - y) \).

### Step-by-Step Solution:

1. **Identify \( x \) and \( y \)**:
Here, we can let \( x = a \) and \( y = (2a + 3b) \). Thus, we can rewrite the expression as:
\[ a^2 - (2a + 3b)^2 \]

2. **Apply the difference of squares formula**:
According to the difference of squares identity:
\[ a^2 - (2a + 3b)^2 = (a + (2a + 3b))(a - (2a + 3b)) \]

3. **Simplify the first factor**:
\[ a + (2a + 3b) = a + 2a + 3b = 3a + 3b \]

4. **Simplify the second factor**:
\[ a - (2a + 3b) = a - 2a - 3b = -a - 3b \]
We can also factor out a negative sign:
\[ - (a + 3b) \]

5. **Combine the factors**:
Now substituting back, we have:
\[ (3a + 3b)(- (a + 3b)) \]
This can be rewritten as:
\[ - (3a + 3b)(a + 3b) \]

6. **Factor out the common term**:
We can factor out 3 from the first factor:
\[ - 3(a + b)(a + 3b) \]

### Final Factorised Form:
Thus, the final factorised form of the expression \( a^2 - (2a + 3b)^2 \) is:
\[ -3(a + 3b)(a + b) \]