Question

which polynomial correctly combines the like terms and puts the given polynomial in standard form?
$-5x^{3}y^{3} + 8x^{4}y^{2} - xy^{5} - 2x^{2}y^{4} + 8x^{6} + 3x^{2}y^{4} - 6xy^{5}$
$\bigcirc -7xy^{5} + 5x^{2}y^{4} - 5x^{3}y^{3} + 8x^{4}y^{2} + 8x^{6}$
$\bigcirc 5xy^{5} + 8x^{4}y^{2} + x^{2}y^{4} - 5x^{3}y^{3} + 8x^{6}$
$\bigcirc 8x^{6} + 5xy^{5} + 8x^{4}y^{2} + x^{2}y^{4} - 5x^{3}y^{3}$
$\bigcirc 8x^{6} + 8x^{4}y^{2} - 5x^{3}y^{3} + x^{2}y^{4} - 7xy^{5}$

Explanation:

Step1: Identify like terms

Like terms: $-xy^5 -6xy^5$; $-2x^2y^4 +3x^2y^4$; others are unique.

Step2: Combine like terms

Combine $xy^5$ terms: $-xy^5 -6xy^5 = -7xy^5$
Combine $x^2y^4$ terms: $-2x^2y^4 +3x^2y^4 = x^2y^4$

Step3: Arrange in standard form

Order by descending total degree of terms:
$8x^6$ (degree 6), $8x^4y^2$ (degree 6), $-5x^3y^3$ (degree 6), $x^2y^4$ (degree 6), $-7xy^5$ (degree 6). When degrees are equal, order by descending exponent of $x$.

Answer:

$8x^6 + 8x^4y^2 - 5x^3y^3 + x^2y^4 - 7xy^5$ (corresponding to the fourth option)