Factorise :
`a-b-4a^(2) + 4b^(2)`

Answer

To factorise the expression \( a - b - 4a^2 + 4b^2 \), we will follow these steps:

### Step 1: Rearrange the terms
Rearranging the terms of the expression gives us:
\[ -4a^2 + 4b^2 + a - b \]

### Step 2: Factor out common terms
We can factor out a negative sign from the first two terms:
\[ -4(a^2 - b^2) + a - b \]

### Step 3: Recognize the difference of squares
The expression \( a^2 - b^2 \) is a difference of squares, which can be factored using the formula \( a^2 - b^2 = (a + b)(a - b) \):
\[ -4((a + b)(a - b)) + a - b \]

### Step 4: Combine like terms
Now we can rewrite the expression:
\[ (a - b) - 4(a + b)(a - b) \]

### Step 5: Factor out the common factor \( (a - b) \)
Now we can factor out \( (a - b) \) from the entire expression:
\[ (a - b)(1 - 4(a + b)) \]

### Final Answer
Thus, the factorised form of the expression \( a - b - 4a^2 + 4b^2 \) is:
\[ (a - b)(1 - 4(a + b)) \]

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