Factorise:
`x ^(2) - xz + xy - yz`

Answer

To factorise the expression \( x^2 - xz + xy - yz \), we can follow these steps:

### Step 1: Group the terms
We can group the terms in pairs to make it easier to factor them. Let's group the first two terms and the last two terms:
\[ (x^2 - xz) + (xy - yz) \]

### Step 2: Factor out the common factors from each group
Now, we will factor out the common factors from each of the grouped terms:
- From the first group \( x^2 - xz \), we can factor out \( x \):
\[ x(x - z) \]
- From the second group \( xy - yz \), we can factor out \( y \):
\[ y(x - z) \]

So now our expression looks like this:
\[ x(x - z) + y(x - z) \]

### Step 3: Factor out the common binomial factor
Now we can see that both terms have a common factor of \( (x - z) \). We can factor that out:
\[ (x - z)(x + y) \]

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

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