What is true about the sum of the two polynomials?

6*s*2*t* – 2*st*2

4*s*2*t* – 3*st*2

The sum is a binomial with a degree of 2.

The sum is a binomial with a degree of 3.

The sum is a trinomial with a degree of 2.

The sum is a trinomial with a degree of 3.

To solve this problem, we need to first find the sum of the two polynomials and then determine the number of terms (binomial or trinomial) and the degree of the resulting polynomial.

Given polynomials:

1. \( 6s^2t - 2st^2 \)
2. \( 4s^2t - 3st^2 \)

### Step 1: Add the two polynomials
To find the sum, add the corresponding terms:

\[
(6s^2t - 2st^2) + (4s^2t - 3st^2)
\]

Combine like terms:

\[
(6s^2t + 4s^2t) + (-2st^2 - 3st^2) = 10s^2t - 5st^2
\]

### Step 2: Determine the number of terms and the degree
- The resulting polynomial is \( 10s^2t - 5st^2 \).
- This polynomial has **two terms** (making it a binomial).
- The degree of each term:
  - \( 10s^2t \) has a degree of \( 2 + 1 = 3 \).
  - \( -5st^2 \) has a degree of \( 1 + 2 = 3 \).

### Conclusion:
- The sum is a **binomial** with a **degree of 3**.

Therefore, the correct statement is: **The sum is a binomial with a degree of 3.**

Would you like more details on this or have any questions? Here are some related questions:

1. How do you determine the degree of a polynomial term?
2. What is the difference between a binomial and a trinomial?
3. Can a polynomial have more than one degree?
4. What is the process for combining like terms in polynomials?
5. How does the degree of a polynomial affect its graph?

**Tip:** Always make sure to combine like terms correctly when adding polynomials to simplify the expression accurately.

Explore the addition of polynomials and understand how to determine the degree and number of terms in the resulting polynomial. This problem involves adding two polynomials and analyzing the degree and classification of the sum. Suitable for high school students.

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