1. **Problem:** Simplify the expression $3a^3b^2 - 5a^3b^2 - 2a^3b^2$. 2. **Formula and rules:** When subtracting or adding like terms, combine coefficients and keep the variables with their exponents unchanged. 3. **Step-by-step solution:** - Identify like terms: $3a^3b^2$, $-5a^3b^2$, and $-2a^3b^2$ all have the same variables and exponents. - Combine coefficients: $3 - 5 - 2 = 3 - \cancel{5} - 2$ (showing cancellation of 5 as subtraction) - Calculate: $3 - 5 = -2$, then $-2 - 2 = -4$ - So, the expression simplifies to: $$-4a^3b^2$$ 4. **Explanation:** Since all terms have the same variables raised to the same powers, we just add or subtract their coefficients. The variables and exponents remain the same. **Final answer:** $$-4a^3b^2$$