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 factoring easier. Let's group them as follows:
\[ (xy + xa) + (yz + za) \]

### Step 2: Factor out the common terms in each group
Now, we can factor out the common factors in each group:
- In the first group \( xy + xa \), the common factor is \( x \).
- In the second group \( yz + za \), the common factor is \( z \).

So, we can rewrite the expression as:
\[ x(y + a) + z(y + a) \]

### Step 3: Factor out the common binomial
Now we can see that \( (y + a) \) is a common factor in both terms:
\[ (x + z)(y + a) \]

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

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