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Alina fully simplifies this polynomial and then writes it in standard form.
[tex]\[ x y^2 - 2 x^2 y + 3 y^3 - 6 x^2 y + 4 x y^2 \][/tex]

If Alina wrote the last term as [tex]\[3 y^3\][/tex], which must be the first term of her polynomial in standard form?

A. [tex]\[ x y^2 \][/tex]

B. [tex]\[ 5 x y^2 \][/tex]

C. [tex]\[ -8 x^2 y \][/tex]

D. [tex]\[ -2 x^2 y \][/tex]



Answer :

GinnyAnswer
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]

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