1. **State the problem:** Simplify the expression $15x^2y - 10xy^3$. 2. **Identify common factors:** Both terms have common factors of $5xy$. 3. **Factor out the common factor:** $$15x^2y - 10xy^3 = 5xy(\cancel{3x} - \cancel{2y^2})$$ Here, $15x^2y = 5xy \times 3x$ and $10xy^3 = 5xy \times 2y^2$. 4. **Write the simplified expression:** $$5xy(3x - 2y^2)$$ 5. **Explanation:** Factoring helps to simplify expressions by extracting the greatest common factor, making it easier to work with or solve further problems.