Fractorise:
`(2a+3b)^(2)-16c ^(2)`

Answer

To factor the expression \((2a + 3b)^2 - 16c^2\), we can follow these steps:

### Step 1: Identify the expression
We start with the expression:
\[ (2a + 3b)^2 - 16c^2 \]
This expression is in the form of \(A^2 - B^2\), where \(A = (2a + 3b)\) and \(B = 4c\).

### Step 2: Apply the difference of squares formula
Recall the difference of squares formula:
\[ A^2 - B^2 = (A + B)(A - B) \]
Using this formula, we can rewrite our expression as:
\[ (2a + 3b + 4c)(2a + 3b - 4c) \]

### Step 3: Write the final factored form
Thus, the factored form of the expression \((2a + 3b)^2 - 16c^2\) is:
\[ (2a + 3b + 4c)(2a + 3b - 4c) \]

### Summary of the solution
The final answer is:
\[ (2a + 3b + 4c)(2a + 3b - 4c) \]

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