To fully simplify the given polynomial, let's combine like terms. The given polynomial is:
[tex]\[ xy^2 - 2x^2y + 3y^3 - 6x^2y + 4xy^2 \][/tex]
Let's identify and combine like terms step by step:
1. Combine [tex]\(xy^2\)[/tex] terms:
[tex]\[ xy^2 + 4xy^2 = 5xy^2 \][/tex]
2. Combine [tex]\(x^2y\)[/tex] terms:
[tex]\[ -2x^2y - 6x^2y = -8x^2y \][/tex]
Now, rewrite the polynomial using these combined terms along with the remaining term [tex]\(3y^3\)[/tex]:
[tex]\[ 3y^3 + 5xy^2 - 8x^2y \][/tex]
This is the polynomial in standard form. According to the problem, Alina wrote the last term as [tex]\(3y^3\)[/tex]. So, the terms in descending order of powers would be:
- [tex]\(3y^3\)[/tex] is the last term
- [tex]\(5xy^2\)[/tex] is the middle term
- [tex]\( -8x^2y \)[/tex] must be the first term
Therefore, the first term in standard form is:
[tex]\[ -8x^2y \][/tex]
So, the correct option is:
[tex]\[ -8x^2y \][/tex]
