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

Explanation:

Step1: Find the difference of the polynomials

$$ \begin{align*} &(a^{3}b + 9a^{2}b^{2}-4ab^{5})-(a^{3}b - 3a^{2}b^{2}+ab^{5})\ =&a^{3}b + 9a^{2}b^{2}-4ab^{5}-a^{3}b + 3a^{2}b^{2}-ab^{5}\ \end{align*} $$

Step2: Combine like - terms

$$ \begin{align*} &(a^{3}b - a^{3}b)+(9a^{2}b^{2}+3a^{2}b^{2})+(-4ab^{5}-ab^{5})\ =&0 + 12a^{2}b^{2}-5ab^{5}\ =&12a^{2}b^{2}-5ab^{5} \end{align*} $$

Step3: Determine the type and degree of the polynomial

  • Type: A binomial (has two terms (12a^{2}b^{2}) and (-5ab^{5}))
  • Degree of (12a^{2}b^{2}): (2 + 2=4)
  • Degree of (-5ab^{5}): (1+5 = 6)

The degree of a polynomial is the highest degree of its terms.

Answer:

The difference is a binomial with a degree of 6.