Question

which polynomial correctly combines the like terms and expresses the given polynomial in standard form?
$9xy^3 - 4y^4 - 10x^2y^2 + x^3y + 3x^4 + 2x^2y^2 - 9y^4$
options:
$-13y^4 + 3x^4 - 8x^2y^2 + x^3y + 9xy^3$
$3x^4 + x^3y - 8x^2y^2 + 9xy^3 - 13y^4$
$-13y^4 + x^3y - 8x^2y^2 + 9xy^3 + 3x^4$

Explanation:

Step1: Identify like terms

Like terms: $-4y^4 -9y^4$, $-10x^2y^2+2x^2y^2$

Step2: Combine like terms

$(-4-9)y^4 = -13y^4$; $(-10+2)x^2y^2=-8x^2y^2$

Step3: Arrange in standard form

Order by descending total degree: $3x^4 + x^3y -8x^2y^2 +9xy^3 -13y^4$

Answer:

$3x^4 + x^3y - 8x^2y^2 + 9xy^3 - 13y^4$