To solve the expression $\left(3a^2 - a + 3\right) + \left(4a^2 - 5\right)$, we need to combine like terms.

Step 1: Identify and combine like terms

• Combine the $a^2$ terms: $3a^2 + 4a^2 = 7a^2$
• Combine the $a$ terms: $-a$ (no other $a$ terms, so it remains $-a$)
• Combine the constant terms: $3 + (-5) = -2$

Step 2: Write the simplified expression

The simplified expression is: $7a^2 - a - 2$

Polynomial Classification:

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

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

Polynomial Classification: Trinomial

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Would you like more details on this, or do you have any other questions? Here are some related questions you might find useful:

1. How do you combine like terms in a polynomial?
2. What makes a polynomial a binomial or a trinomial?
3. Can you classify a polynomial with more than three terms?
4. What are some examples of binomials and trinomials in algebra?
5. How do you subtract polynomials instead of adding them?

Tip: When combining like terms, always align the terms by their degree (exponent) to avoid mistakes.