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

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:

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

Now, you can combine the like terms:

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

The fully simplified form of the expression is:

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

Would you like more details or have any questions?

Here are some related questions:

1. How do you factor a difference of squares?
2. What is the process for multiplying polynomials?
3. How do you expand \((x + y)^2\)?
4. Can you simplify \((x^2 - y^2)\) without using the difference of squares?
5. What are some common types of polynomial factorizations?

**Tip:** When simplifying expressions, always look for common factoring patterns like the difference of squares or perfect square trinomials.

Understand how to simplify the expression (x^2 - y^2) * x * (x + y) step-by-step. Learn about factoring, the difference of squares, and polynomial multiplication in algebra. Suitable for high school students and beyond.

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