Find the sum or difference. Classify you answer as a binomial or a trinomial.

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

Simplified Expression :

Polynomial Classification :

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.

Learn how to find the sum or difference of polynomials by simplifying the expression (3a^2 - a + 3) + (4a^2 - 5). Understand the process of combining like terms and classify the result as a binomial or trinomial. Suitable for Grades 7-9 students studying algebraic expressions and polynomial operations.

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