Factorise :
`16x^(2) - y^(2) + 4yz - 4z^(2)`

Answer

To factorise the expression \( 16x^2 - y^2 + 4yz - 4z^2 \), we can follow these steps:

### Step 1: Rearrange the expression
We start by rearranging the terms for clarity:
\[ 16x^2 - (y^2 - 4yz + 4z^2) \]

### Step 2: Recognize the perfect square
The expression \( y^2 - 4yz + 4z^2 \) can be recognized as a perfect square trinomial. It can be factored as:
\[ y^2 - 4yz + 4z^2 = (y - 2z)^2 \]

### Step 3: Substitute back into the expression
Now substitute the factored form back into the expression:
\[ 16x^2 - (y - 2z)^2 \]

### Step 4: Apply the difference of squares formula
The expression \( 16x^2 - (y - 2z)^2 \) is a difference of squares, which can be factored using the formula \( a^2 - b^2 = (a - b)(a + b) \). Here, \( a = 4x \) and \( b = (y - 2z) \):
\[ 16x^2 - (y - 2z)^2 = (4x - (y - 2z))(4x + (y - 2z)) \]

### Step 5: Simplify the factors
Now, simplify the factors:
\[ (4x - y + 2z)(4x + y - 2z) \]

### Final Answer
Thus, the factorised form of the expression \( 16x^2 - y^2 + 4yz - 4z^2 \) is:
\[ (4x - y + 2z)(4x + y - 2z) \]