julian fully simplifies this polynomial and then writes it in standard form.\n$4x^{2}y^{2}-2y^{4}-8xy^{3}+9x^…

julian fully simplifies this polynomial and then writes it in standard form.\n$4x^{2}y^{2}-2y^{4}-8xy^{3}+9x^{3}y + 6y^{4}-2xy^{3}-3x^{4}+x^{2}y^{2}$\nif julian wrote the last term as $-3x^{4}$, which must be the first term of his polynomial in standard form?\n$4y^{4}$\n$6y^{4}$\n$-2xy^{3}$\n$-10xy^{3}$

julian fully simplifies this polynomial and then writes it in standard form.\n$4x^{2}y^{2}-2y^{4}-8xy^{3}+9x^{3}y + 6y^{4}-2xy^{3}-3x^{4}+x^{2}y^{2}$\nif julian wrote the last term as $-3x^{4}$, which must be the first term of his polynomial in standard form?\n$4y^{4}$\n$6y^{4}$\n$-2xy^{3}$\n$-10xy^{3}$

Answer

Answer:

B. $6y^{4}$

Explanation:

Step1: Combine like - terms

Combine the terms with the same variables and exponents. For the $y^{4}$ terms: $- 2y^{4}+6y^{4}=4y^{4}$ For the $x^{2}y^{2}$ terms: $4x^{2}y^{2}+x^{2}y^{2}=5x^{2}y^{2}$ For the $xy^{3}$ terms: $-8xy^{3}-2xy^{3}=-10xy^{3}$ The polynomial becomes $5x^{2}y^{2}+4y^{4}-10xy^{3}+9x^{3}y - 3x^{4}$

Step2: Write in standard form

In a polynomial in two variables $x$ and $y$, the standard form is written in descending order of the sum of the exponents of the variables in each term. The sum of exponents for $5x^{2}y^{2}$ is $2 + 2=4$, for $4y^{4}$ is $4$, for $-10xy^{3}$ is $1+3 = 4$, for $9x^{3}y$ is $3 + 1=4$ and for $-3x^{4}$ is $4$. We compare the coefficients and the order of variables. The term with the highest - degree (in terms of the sum of exponents) and considering the alphabetical order of variables ($x$ before $y$ when the sum of exponents is the same) among the non - $-3x^{4}$ terms is $6y^{4}$ (from the combination step). When writing the polynomial in standard form, if the last term is $-3x^{4}$, the first term is $6y^{4}$ as it has the highest degree among the non - $-3x^{4}$ terms and is consistent with the rules of writing polynomials in standard form.