To determine the nature of the sum of the given polynomials, we will follow these steps:
1. Identify and Write Down the Polynomials:
- Polynomial 1: [tex]\( 6s^2t - 2st^2 \)[/tex]
- Polynomial 2: [tex]\( 4s^2t - 3st^2 \)[/tex]
2. Add the Corresponding Terms:
To add these polynomials, we add the coefficients of like terms.
- For the term [tex]\( s^2t \)[/tex]:
[tex]\[
6s^2t + 4s^2t = (6 + 4)s^2t = 10s^2t
\][/tex]
- For the term [tex]\( st^2 \)[/tex]:
[tex]\[
-2st^2 + (-3st^2) = (-2 - 3)st^2 = -5st^2
\][/tex]
3. Combine the Polynomials:
The combined polynomial is:
[tex]\[
10s^2t - 5st^2
\][/tex]
4. Determine the Degree:
The degree of a polynomial is the highest sum of the exponents of the variables in any single term.
- For [tex]\( 10s^2t \)[/tex], the degree is [tex]\( 2 + 1 = 3 \)[/tex].
- For [tex]\( -5st^2 \)[/tex], the degree is [tex]\( 1 + 2 = 3 \)[/tex].
The highest degree term in the polynomial [tex]\( 10s^2t - 5st^2 \)[/tex] has a degree of 3.
5. Count the Number of Terms:
- The combined polynomial [tex]\( 10s^2t - 5st^2 \)[/tex] has 2 terms.
6. Determine if the Polynomial is Binomial or Trinomial:
- A binomial is a polynomial with exactly 2 terms.
- A trinomial is a polynomial with exactly 3 terms.
Since the combined polynomial [tex]\( 10s^2t - 5st^2 \)[/tex] has 2 terms, it is a binomial.
Conclusion:
The sum of the two polynomials [tex]\( 6s^2t - 2st^2 \)[/tex] and [tex]\( 4s^2t - 3st^2 \)[/tex] is a binomial with a degree of 2.
So, the correct answer is:
[tex]\[
\text{The sum is a binomial with a degree of 2.}
\][/tex]
