Factorise `2x+4y-8xy-1`

Explanation

To factorise the expression \(2x + 4y - 8xy - 1\), we can follow these steps:

### Step 1: Rearrange the Expression
First, we can rearrange the terms for easier grouping:
\[ 2x - 1 + 4y - 8xy \]

### Step 2: Group the Terms
Now, we can group the terms in pairs:
\[ (2x - 1) + (4y - 8xy) \]

### Step 3: Factor Out Common Terms
Next, we factor out the common terms from each group:
- From the first group \(2x - 1\), we can take it as it is.
- From the second group \(4y - 8xy\), we can factor out \(4y\):
\[ = (2x - 1) + 4y(1 - 2x) \]

### Step 4: Rearranging the Second Factor
Notice that \(1 - 2x\) can be rewritten as \(-(2x - 1)\):
\[ = (2x - 1) - 4y(2x - 1) \]

### Step 5: Factor Out the Common Binomial
Now, we can factor out the common binomial factor \((2x - 1)\):
\[ = (2x - 1)(1 - 4y) \]

### Final Answer
Thus, the factorised form of the expression \(2x + 4y - 8xy - 1\) is:
\[ (2x - 1)(1 - 4y) \]

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