Factorise : `x^2+y-xy-x`

Explanation

To factorize the expression \( x^2 + y - xy - x \), we can follow these steps:

### Step 1: Rearrange the expression
Rearranging the terms can help us see common factors more clearly. We can rewrite the expression as:
\[ x^2 - x - xy + y \]

### Step 2: Group the terms
Next, we can group the terms into two pairs:
\[ (x^2 - x) + (-xy + y) \]

### Step 3: Factor out common factors from each group
Now, we will factor out the common factors from each group:
- From the first group \( (x^2 - x) \), we can factor out \( x \):
\[ x(x - 1) \]
- From the second group \( (-xy + y) \), we can factor out \( -y \):
\[ -y(x - 1) \]

### Step 4: Combine the factored terms
Now we can combine the factored terms:
\[ x(x - 1) - y(x - 1) \]

### Step 5: Factor out the common binomial factor
We notice that \( (x - 1) \) is a common factor in both terms:
\[ (x - 1)(x - y) \]

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

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