`x ^(2) - xz + xy - yz =? `

Options

A. `(x-y)(x+z)`
B. `(x -y) (x -z)`
C. `(x +y) (x -z)`
D. `(x -y) (z-x)`

Answer

To factor 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 factoring easier:
\[ (x^2 - xz) + (xy - yz) \]

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

### Step 3: Combine the factored terms
Now we can combine the factored terms:
\[ x(x - z) + y(x - z) \]

### Step 4: Factor out the common binomial
Notice that \( (x - z) \) is common in both terms, so we can factor that out:
\[ (x - z)(x + y) \]

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

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