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

which is true about the completely simplified difference of the polynomials $6x^{6}-x^{3}y^{4}-5xy^{5}$ and $4x^{5}y + 2x^{3}y^{4}+5xy^{5}$?\nthe difference has 3 terms and a degree of 6.\nthe difference has 4 terms and a degree of 6.\nthe difference has 3 terms and a degree of 7.\nthe difference has 4 terms and a degree of 7.

which is true about the completely simplified difference of the polynomials $6x^{6}-x^{3}y^{4}-5xy^{5}$ and $4x^{5}y + 2x^{3}y^{4}+5xy^{5}$?\nthe difference has 3 terms and a degree of 6.\nthe difference has 4 terms and a degree of 6.\nthe difference has 3 terms and a degree of 7.\nthe difference has 4 terms and a degree of 7.

Answer

Explanation:

Step1: Find the difference of 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

$=6x^{6}+(-x^{3}y^{4}-2x^{3}y^{4})+(-5xy^{5}-5xy^{5})-4x^{5}y=6x^{6}-3x^{3}y^{4}-10xy^{5}-4x^{5}y$

Step3: Determine the number of terms and degree

The polynomial $6x^{6}-3x^{3}y^{4}-10xy^{5}-4x^{5}y$ has 4 terms. The degree of a term in a multi - variable polynomial $a x^{m}y^{n}$ is $m + n$. The degrees of the terms $6x^{6}$ (degree 6), $-3x^{3}y^{4}$ (degree 3 + 4=7), $-10xy^{5}$ (degree 1+5 = 6), $-4x^{5}y$ (degree 5 + 1=6) respectively. The highest degree among the terms is 7.

Answer:

The difference has 4 terms and a degree of 7.