which is true about the completely simplified difference of the polynomials $a^{3}b + 9a^{2}b^{2}-4ab^{5}$…

which is true about the completely simplified difference of the polynomials $a^{3}b + 9a^{2}b^{2}-4ab^{5}$ and $a^{3}b - 3a^{2}b^{2}+ab^{5}$?\nthe difference is a binomial with a degree of 5.\nthe difference is a binomial with a degree of 6.\nthe difference is a trinomial with a degree of 5.\nthe difference is a trinomial with a degree of 6.

which is true about the completely simplified difference of the polynomials $a^{3}b + 9a^{2}b^{2}-4ab^{5}$ and $a^{3}b - 3a^{2}b^{2}+ab^{5}$?\nthe difference is a binomial with a degree of 5.\nthe difference is a binomial with a degree of 6.\nthe difference is a trinomial with a degree of 5.\nthe difference is a trinomial with a degree of 6.

Answer

Answer:

The difference is a binomial with a degree of 6.

Explanation:

Step1: Find the difference of the polynomials

$(a^{3}b + 9a^{2}b^{2}-4ab^{5})-(a^{3}b - 3a^{2}b^{2}+ab^{5})$ $=a^{3}b + 9a^{2}b^{2}-4ab^{5}-a^{3}b + 3a^{2}b^{2}-ab^{5}$

Step2: Combine like - terms

$(a^{3}b - a^{3}b)+(9a^{2}b^{2}+ 3a^{2}b^{2})+(-4ab^{5}-ab^{5})$ $=0 + 12a^{2}b^{2}-5ab^{5}$ $=12a^{2}b^{2}-5ab^{5}$

Step3: Determine the type and degree

The resulting polynomial $12a^{2}b^{2}-5ab^{5}$ is a binomial (has two terms). The degree of a term in a two - variable polynomial $ax^{m}y^{n}$ is $m + n$. For the term $12a^{2}b^{2}$, the degree is $2 + 2=4$. For the term $-5ab^{5}$, the degree is $1+5 = 6$. The degree of the polynomial is the highest degree of its terms, which is 6.