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.