Fractorise:
`36c ^(2) - (5a+b)^(2)`

Answer

To factorize the expression \( 36c^2 - (5a + b)^2 \), we can use the difference of squares formula, which states that \( A^2 - B^2 = (A - B)(A + B) \).

### Step-by-Step Solution:

1. **Identify the squares**:
- We can rewrite \( 36c^2 \) as \( (6c)^2 \).
- We can rewrite \( (5a + b)^2 \) as it is.

So, we have:
\[ 36c^2 - (5a + b)^2 = (6c)^2 - (5a + b)^2 \]

2. **Apply the difference of squares formula**:
Using the formula \( A^2 - B^2 = (A - B)(A + B) \), we can set:
- \( A = 6c \)
- \( B = 5a + b \)

Therefore, we can write:
\[ (6c - (5a + b))(6c + (5a + b)) \]

3. **Simplify the expression**:
Now, we simplify the factors:
- The first factor becomes \( 6c - 5a - b \).
- The second factor becomes \( 6c + 5a + b \).

So, we have:
\[ (6c - 5a - b)(6c + 5a + b) \]

### Final Answer:
The factorized form of \( 36c^2 - (5a + b)^2 \) is:
\[ (6c - 5a - b)(6c + 5a + b) \]