Let's solve the second expression and classify it.

Expression:

$\large \left(3a^2 + 4a + 5\right) - \left(2a^2 - 3a + 1\right)$

Step 1: Distribute the negative sign to the second polynomial

$3a^2 + 4a + 5 - 2a^2 + 3a - 1$

Step 2: Combine like terms

• Combine the $a^2$ terms: $3a^2 - 2a^2 = 1a^2$ or simply $a^2$
• Combine the $a$ terms: $4a + 3a = 7a$
• Combine the constant terms: $5 - 1 = 4$

Step 3: Write the simplified expression

$a^2 + 7a + 4$

Polynomial Classification:

The simplified expression has three terms: $a^2$, $7a$, and $4$. Therefore, it is classified as a trinomial.

---

Simplified Expression: $\mathbf{a^2 + 7a + 4}$

Polynomial Classification: Trinomial

---

Would you like to go over any specific part of this? Here are some related questions that might interest you:

1. How do you handle subtraction when simplifying polynomials?
2. What are the differences between addition and subtraction in polynomial operations?
3. How does the degree of a polynomial affect its classification?
4. What happens when you add or subtract polynomials of different degrees?
5. How do you simplify polynomials involving more complex terms, like those with higher degrees?

Tip: Always be careful with the signs when subtracting polynomials. Distributing the negative sign correctly is crucial to getting the right answer.