which statement is true about the polynomial -10m^4n^3 + 8m^2n^6 + 3m^4n^3 - 2m^2n^6 - 6m^2n^6 after it has…
which statement is true about the polynomial -10m^4n^3 + 8m^2n^6 + 3m^4n^3 - 2m^2n^6 - 6m^2n^6 after it has been fully simplified?\nit is a monomial with a degree of 4.\nit is a monomial with a degree of 7.\nit is a binomial with a degree of 6.\nit is a binomial with a degree of 8.
Answer
Explanation:
Step1: Combine like - terms
Combine the terms with the same variables and exponents. For the terms with $m^{4}n^{3}$: $- 10m^{4}n^{3}+3m^{4}n^{3}=(-10 + 3)m^{4}n^{3}=-7m^{4}n^{3}$. For the terms with $m^{2}n^{6}$: $8m^{2}n^{6}-2m^{2}n^{6}-6m^{2}n^{6}=(8 - 2-6)m^{2}n^{6}=0$. So the simplified polynomial is $-7m^{4}n^{3}$.
Step2: Determine the type and degree
A monomial is a polynomial with one term, and the degree of a monomial in two variables $m$ and $n$ is the sum of the exponents of the variables. Here, the degree of $-7m^{4}n^{3}$ is $4 + 3=7$.
Answer:
It is a monomial with a degree of 7.