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

Options

A. `(x - 1) (x + y)`
B. `(x +1) (x + y)`
C. `(x -1) (x - y)`
D. None of these

Answer

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

### Step 1: Rearrange the expression
First, let's rearrange the expression for clarity:
\[ x^2 - x - xy + y \]

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

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

Putting it all together, we have:
\[ x(x - 1) - y(x - 1) \]

### Step 4: Factor out the common binomial factor
Now, we can see that \( (x - 1) \) is a common factor:
\[ (x - 1)(x - y) \]

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

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