The problem asks us to factorize the expression $x + y - ax - ay$. We need to choose the correct factorization from the given options.

1. Problem Description

The problem asks us to factorize the expression $x + y - ax - ay$. We need to choose the correct factorization from the given options.

2. Solution Steps

We are given the expression $x + y - ax - ay$.

We can group the terms as follows:

$(x + y) - (ax + ay)$.

Now, we can factor out a common term from each group.

From the first group, $(x + y)$, we can't factor anything out.

From the second group, $(ax + ay)$, we can factor out $a$, resulting in $a(x + y)$.

So, we have $(x + y) - a(x + y)$.

Now, we can factor out the common term $(x + y)$ from the entire expression:

$(x + y)(1 - a)$.

3. Final Answer

The factored form of the expression $x + y - ax - ay$ is $(x + y)(1 - a)$.

Therefore, the correct answer is C.

Final Answer: C