which statement is true about the polynomial $5s^{6}t^{2}+6st^{9}-8s^{6}t^{2}-6t^{7}$ after it has been…

Explanation:

Step1: Combine like - terms

Combine the terms with the same variables and exponents. The like - terms are $5s^{6}t^{2}$ and $-8s^{6}t^{2}$. $(5s^{6}t^{2}-8s^{6}t^{2})+6st^{9}-6t^{7}=- 3s^{6}t^{2}+6st^{9}-6t^{7}$

Step2: Determine the number of terms

The simplified polynomial $-3s^{6}t^{2}+6st^{9}-6t^{7}$ has 3 terms: $-3s^{6}t^{2}$, $6st^{9}$, and $-6t^{7}$.

Step3: Determine the degree

The degree of a term in a polynomial with two variables $s$ and $t$ is the sum of the exponents of the variables in that term. For the term $-3s^{6}t^{2}$, the degree is $6 + 2=8$. For the term $6st^{9}$, the degree is $1+9 = 9$. For the term $-6t^{7}$, the degree is 7. The highest degree among the terms is 9.

Answer:

It has 3 terms and a degree of 9.