The given expression is \((x^2 - y^2)(x + y)\).

First, recognize that \(x^2 - y^2\) is a difference of squares, which can be factored as:

\[
x^2 - y^2 = (x - y)(x + y)
\]

So, the expression becomes:

\[
(x - y)(x + y)(x + y)
\]

This can be further simplified by combining the like terms:

\[
(x - y) \cdot (x + y)^2
\]

Thus, the fully simplified form of the expression is:

\[
(x - y) \cdot (x + y)^2
\]

Would you like more details or have any questions?

Here are some related questions:

1. What is the general formula for the difference of squares?
2. How do you expand and simplify \((x + y)^2\)?
3. Can \((x - y) \cdot (x + y)^2\) be expanded further?
4. What are the steps to factor a polynomial completely?
5. How does the distributive property apply in polynomial multiplication?

**Tip:** When multiplying polynomials, always factor them as much as possible before combining like terms. This often simplifies the process.

Learn how to factorize the expression (x^2 - y^2)(x + y) step-by-step using the difference of squares formula. This problem explores polynomial factorization techniques, suitable for advanced high school students.

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