find the sum or difference. then identify the degree of the sum or difference and classify the polynomial by the number of terms. for this equation. (3x^2 + 6x) + (4x^2 - 8x)

Let's break down and solve the given polynomial expression:

### Step 1: Combine like terms
The given expression is:

\[
(3x^2 + 6x) + (4x^2 - 8x)
\]

Now, let's combine the like terms:

1. Combine the \(x^2\) terms:
   \[
   3x^2 + 4x^2 = 7x^2
   \]
   
2. Combine the \(x\) terms:
   \[
   6x - 8x = -2x
   \]

Thus, the resulting polynomial is:

\[
7x^2 - 2x
\]

### Step 2: Identify the degree of the polynomial
The degree of a polynomial is the highest power of \(x\) in the expression. In this case, the highest power of \(x\) is \(x^2\), so the degree is:

\[
\text{Degree} = 2
\]

### Step 3: Classify by the number of terms
This polynomial has two terms: \(7x^2\) and \(-2x\). A polynomial with two terms is called a **binomial**.

### Final Answer:
- **Sum/Difference**: \(7x^2 - 2x\)
- **Degree**: 2
- **Classification**: Binomial

Would you like further details or have any questions?

Here are 5 related questions to explore further:
1. What is the degree of a constant term polynomial?
2. How do you combine like terms in polynomials with higher powers?
3. What would the polynomial look like if one of the terms was cubic?
4. Can a binomial have a degree of 3 or higher?
5. What are the steps for multiplying two binomials?

**Tip:** When combining polynomials, always focus on matching the powers of variables to simplify accurately.

Learn how to find the sum or difference of polynomials (3x^2 + 6x) + (4x^2 - 8x) and identify the degree and classification of the resulting polynomial. This problem covers key algebraic concepts including combining like terms, polynomial degrees, and classifications. Suitable for students in Grades 7-9.

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