Fractorise:
`16(2p-3q)^(2) -4 (2p - 3q)`

Answer

To factorise the expression \( 16(2p - 3q)^2 - 4(2p - 3q) \), we can follow these steps:

### Step 1: Identify the common factor
We can see that both terms in the expression share a common factor of \( (2p - 3q) \).

### Step 2: Factor out the common term
We can factor out \( (2p - 3q) \) from the expression:
\[ 16(2p - 3q)^2 - 4(2p - 3q) = (2p - 3q)(16(2p - 3q) - 4) \]

### Step 3: Simplify the expression inside the parentheses
Now, we simplify the expression inside the parentheses:
\[ 16(2p - 3q) - 4 \]
This can be simplified to:
\[ 16(2p - 3q) - 4 = 16(2p - 3q) - 4 \cdot 1 \]

### Step 4: Rewrite the expression
So the expression becomes:
\[ (2p - 3q)(16(2p - 3q) - 4) \]

### Step 5: Factor further if possible
Now, we can factor out the constant from the second term:
\[ (2p - 3q)(4(4(2p - 3q) - 1)) \]

### Final Factorized Form
Thus, the final factorized form of the expression is:
\[ 4(2p - 3q)(4(2p - 3q) - 1) \]