which is true about the completely simplified difference of the polynomials (6x^{6}-x^{3}y^{4}-5xy^{5}) and…

Explanation:

Step1: Find the difference of the polynomials

$$(6x^{6}-x^{3}y^{4}-5xy^{5})-(4x^{5}y + 2x^{3}y^{4}+5xy^{5})$$ $$=6x^{6}-x^{3}y^{4}-5xy^{5}-4x^{5}y - 2x^{3}y^{4}-5xy^{5}$$

Step2: Combine like - terms

For the $x^{3}y^{4}$ terms: $-x^{3}y^{4}-2x^{3}y^{4}=-3x^{3}y^{4}$ For the $xy^{5}$ terms: $-5xy^{5}-5xy^{5}=-10xy^{5}$ The polynomial becomes $6x^{6}-4x^{5}y-3x^{3}y^{4}-10xy^{5}$

Step3: Determine the number of terms and degree

The polynomial $6x^{6}-4x^{5}y-3x^{3}y^{4}-10xy^{5}$ has 4 terms. The degree of a term in a polynomial with two variables $x$ and $y$ is the sum of the exponents of $x$ and $y$ in that term. For the term $6x^{6}$, degree is 6. For the term $-4x^{5}y$, degree is $5 + 1=6$. For the term $-3x^{3}y^{4}$, degree is $3+4 = 7$. For the term $-10xy^{5}$, degree is $1 + 5=6$. The highest degree among the terms is 7.

Answer:

The difference has 4 terms and a degree of 7.