Let's go through each expression and match it with its correct factorization.

1. $x^2 - y^2$
   This is a difference of squares, which can be factored as: $x^2 - y^2 = (x + y)(x - y)$

2. $x^3 - y^3$
   This is a difference of cubes, which can be factored as: $x^3 - y^3 = (x - y)(x^2 + xy + y^2)$

3. $x^3 + y^3$
   This is a sum of cubes, which can be factored as: $x^3 + y^3 = (x + y)(x^2 - xy + y^2)$

4. $x^2 + 2xy + y^2$
   This is a perfect square trinomial, which can be factored as: $x^2 + 2xy + y^2 = (x + y)^2$

Summary:

• $x^2 - y^2 = (x + y)(x - y)$
• $x^3 - y^3 = (x - y)(x^2 + xy + y^2)$
• $x^3 + y^3 = (x + y)(x^2 - xy + y^2)$
• $x^2 + 2xy + y^2 = (x + y)^2$

Would you like further clarification or examples?

---

Related Questions:

1. How do you factor $x^4 - y^4$?
2. What is the factorization of $x^2 + y^2$?
3. Can $x^2 - 4xy + 4y^2$ be factored as a perfect square?
4. How do you recognize a sum of cubes versus a difference of cubes?
5. How can you expand $(x - y)^2$ to verify its factors?

Tip: Remember, differences of squares, cubes, and perfect squares have specific patterns that simplify factorization!