1. **State the problem:** Factorize the expression $ax + ay + bx + by$. 2. **Group terms:** Group the terms to factor by common factors: $$ax + ay + bx + by = (ax + ay) + (bx + by)$$ 3. **Factor out common factors in each group:** $$= a(x + y) + b(x + y)$$ 4. **Factor out the common binomial factor:** $$= (a + b)(x + y)$$ 5. **Conclusion:** The factorized form of $ax + ay + bx + by$ is $$(a + b)(x + y)$$. This matches option B.