Question

which polynomial correctly combines the like terms and expresses the given polynomial in standard form?
$8mn^5 - 2m^6 + 5m^2n^4 - m^3n^3 + n^6 - 4m^6 + 9m^2n^4 - mn^5 - 4m^3n^3$

Explanation:

Step1: Group like $m^6$ terms

$-2m^6 -4m^6 = (-2-4)m^6 = -6m^6$

Step2: Group like $m^2n^4$ terms

$5m^2n^4 +9m^2n^4 = (5+9)m^2n^4 = 14m^2n^4$

Step3: Group like $mn^5$ terms

$8mn^5 -mn^5 = (8-1)mn^5 = 7mn^5$

Step4: Identify unpaired terms

$-m^3n^3 -4m^3n^3 = (-1-4)m^3n^3 = -5m^3n^3$; $n^6$ has no like terms

Step5: Arrange in standard form (descending total degree)

$n^6 + 7mn^5 + 14m^2n^4 -5m^3n^3 -6m^6$

Answer:

$n^6 + 7mn^5 + 14m^2n^4 - 5m^3n^3 - 6m^6$