1. **Problem 1:** Simplify $2b^4 - 3b^3 + 4b^4$ and classify the result. 2. Combine like terms: $2b^4 + 4b^4 = 6b^4$ and keep $-3b^3$ as is. 3. The expression becomes $$6b^4 - 3b^3$$. 4. This expression has two terms, so it is a **binomial**. 5. **Problem 2:** Simplify $2x^2 + 5y - 3x^2 - 5y$ and classify the result. 6. Combine like terms: $2x^2 - 3x^2 = \cancel{2x^2} - \cancel{3x^2} = -x^2$ and $5y - 5y = \cancel{5y} - \cancel{5y} = 0$. 7. The expression simplifies to $$-x^2$$. 8. This expression has one term, so it is a **monomial**. 9. **Problem 3:** Simplify $6c^3 - 8c^2 - 4c^3 + 7c^2 - 4c + 3$ and classify the result. 10. Combine like terms: $6c^3 - 4c^3 = \cancel{6c^3} - \cancel{4c^3} = 2c^3$ and $-8c^2 + 7c^2 = \cancel{-8c^2} + \cancel{7c^2} = -c^2$. 11. The expression becomes $$2c^3 - c^2 - 4c + 3$$. 12. This expression has four terms, so it is **none of these** (not monomial, binomial, or trinomial). **Final answers:** - Problem 1: $6b^4 - 3b^3$, binomial - Problem 2: $-x^2$, monomial - Problem 3: $2c^3 - c^2 - 4c + 3$, none of these