what is true about the completely simplified sum of the polynomials $3x^{2}y^{2}-2xy^{5}$ and…

what is true about the completely simplified sum of the polynomials $3x^{2}y^{2}-2xy^{5}$ and $-3x^{2}y^{2}+3x^{4}y$?\nthe sum is a trinomial with a degree of 5.\nthe sum is a trinomial with a degree of 6.\nthe sum is a binomial with a degree of 5.\nthe sum is a binomial with a degree of 6.

what is true about the completely simplified sum of the polynomials $3x^{2}y^{2}-2xy^{5}$ and $-3x^{2}y^{2}+3x^{4}y$?\nthe sum is a trinomial with a degree of 5.\nthe sum is a trinomial with a degree of 6.\nthe sum is a binomial with a degree of 5.\nthe sum is a binomial with a degree of 6.

Answer

Answer:

D. The sum is a binomial with a degree of 6.

Explanation:

Step1: Find the sum of polynomials

$(3x^{2}y^{2}-2xy^{5})+(-3x^{2}y^{2}+3x^{4}y)$ $=3x^{2}y^{2}-2xy^{5}-3x^{2}y^{2}+3x^{4}y$ $=(3x^{2}y^{2}-3x^{2}y^{2})-2xy^{5}+3x^{4}y$ $=- 2xy^{5}+3x^{4}y$

Step2: Determine the type of polynomial

The resulting polynomial $-2xy^{5}+3x^{4}y$ has two terms, so it is a binomial.

Step3: Calculate the degree

For the term $-2xy^{5}$, the degree is $1 + 5=6$. For the term $3x^{4}y$, the degree is $4+1 = 5$. The highest - degree among the terms is 6. So the degree of the polynomial is 6.