The factor form `xy+yz+xa+za` is

Options

A. `xz+ya`
B. `(x+z)(y+a)`
C. `xy+za`
D. `(x+a)(y+z)`

Answer

To factor the expression \( xy + yz + xa + za \), we can follow these steps:

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

### Step 2: Factor out the common factors
Now, we can factor out the common factors from each group:
- From the first group \( xy + yz \), we can factor out \( y \):
\[ y(x + z) \]
- From the second group \( xa + za \), we can factor out \( a \):
\[ a(x + z) \]

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

### Step 4: Factor out the common binomial
Notice that \( (x + z) \) is common in both terms. We can factor it out:
\[ (x + z)(y + a) \]

### Final Result
Thus, the factor form of the expression \( xy + yz + xa + za \) is:
\[ (x + z)(y + a) \]