The factors of `x^2+xy-2xz-2yz`are

Options

A. (x-y)(x+2z)
B. (x+y)(x-2z)
C. (x-y)(x-2z)
D. (x+y)(x+2z)

Answer

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

### Step 1: Group the terms
We can group the terms in pairs to make factoring easier:
\[ (x^2 + xy) + (-2xz - 2yz) \]

### Step 2: Factor out common factors from each group
In the first group \( (x^2 + xy) \), we can factor out \( x \):
\[ x(x + y) \]
In the second group \( (-2xz - 2yz) \), we can factor out \( -2z \):
\[ -2z(x + y) \]

### Step 3: Combine the factored groups
Now we can combine the two factored groups:
\[ x(x + y) - 2z(x + y) \]

### Step 4: Factor out the common binomial factor
Notice that \( (x + y) \) is a common factor:
\[ (x + y)(x - 2z) \]

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

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