To simplify \( g(x) = (x - y)(x^2 + y^2) \), we can expand the expression by distributing \( (x - y) \) to each term inside the parentheses.

Here are the steps:

1. **Distribute \( x \) to \( (x^2 + y^2) \):**

\[
x \cdot (x^2 + y^2) = x^3 + xy^2
\]

2. **Distribute \( -y \) to \( (x^2 + y^2) \):**

\[
-y \cdot (x^2 + y^2) = -yx^2 - y^3
\]

3. **Combine the results:**

\[
g(x) = x^3 + xy^2 - yx^2 - y^3
\]

Therefore, the simplified form of \( g(x) \) is:

\[
g(x) = x^3 + xy^2 - yx^2 - y^3
\]

Would you like more details or have any questions about the steps involved?

Here are 5 questions you might want to ask next:
1. Can you simplify more complex expressions involving multiple variables?
2. How do you factor polynomials like the result we got?
3. What are the common mistakes to avoid when distributing terms?
4. How can this simplified expression be used in solving equations?
5. What are the steps to expand binomials raised to higher powers?

**Tip:** Always carefully distribute each term in parentheses to ensure accuracy when simplifying expressions.

Learn how to simplify the expression (x - y)(x^2 + y^2) with detailed steps. This problem involves algebraic manipulation and distribution of terms, suitable for high school students (Grades 10-12).

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