Answered

IDNLearn.com: Your reliable source for finding expert answers. Whether it's a simple query or a complex problem, our experts have the answers you need.

Julian fully simplifies this polynomial and then writes it in standard form.

[tex]\[ 4x^2 y^2 - 2y^4 - 8xy^3 + 9x^3 y + 6y^4 - 2xy^3 - 3x^4 + x^2 y^2 \][/tex]

If Julian wrote the last term as [tex]\(-3x^4\)[/tex], which must be the first term of his polynomial in standard form?

A. [tex]\(4y^4\)[/tex]
B. [tex]\(6y^4\)[/tex]
C. [tex]\(-2xy^3\)[/tex]
D. [tex]\(-10xy^3\)[/tex]

Sagot :

GinnyAnsweridn
Let's start by fully simplifying the given polynomial by combining like terms:

The polynomial is:
[tex]\[ 4x^2y^2 - 2y^4 - 8xy^3 + 9x^3y + 6y^4 - 2xy^3 - 3x^4 + x^2y^2 \][/tex]

First, we group like terms together:

### Grouping the like terms:

1. [tex]\(x^4\)[/tex] terms:
[tex]\[ -3x^4 \][/tex]

2. [tex]\(x^3y\)[/tex] terms:
[tex]\[ 9x^3y \][/tex]

3. [tex]\(x^2y^2\)[/tex] terms:
[tex]\[ 4x^2y^2 + x^2y^2 = 5x^2y^2 \][/tex]

4. [tex]\(xy^3\)[/tex] terms:
[tex]\[ -8xy^3 - 2xy^3 = -10xy^3 \][/tex]

5. [tex]\(y^4\)[/tex] terms:
[tex]\[ -2y^4 + 6y^4 = 4y^4 \][/tex]

So, the simplified polynomial is:
[tex]\[ -3x^4 + 9x^3y + 5x^2y^2 - 10xy^3 + 4y^4 \][/tex]

Julian wrote the last term as [tex]\( -3x^4 \)[/tex]. In standard form, the polynomial is arranged in descending order of the powers of x and y. Therefore, the first term should be the one with the highest power of y, which is:

[tex]\[ 4y^4 \][/tex]

Thus, the correct answer is:

[tex]\[ 4y^4 \][/tex]
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! IDNLearn.com has the solutions you’re looking for. Thanks for visiting, and see you next time for more reliable information.