1. **State the problem:** Simplify the expression $xy^2 + yx^2$. 2. **Identify common factors:** Notice that both terms contain the factors $x$ and $y$. 3. **Factor out the common terms:** $$xy^2 + yx^2 = xy^2 + xyx = x y^2 + x^2 y$$ We can factor out $xy$: $$xy^2 + x^2 y = xy(y + x)$$ 4. **Final simplified form:** $$xy(y + x)$$ This is the simplest factorization of the given expression. **Explanation:** We looked for common factors in both terms and factored them out to simplify the expression. This helps in understanding the structure and can be useful for further operations like solving equations or integration.