Question

Which polynomial correctly combines the like terms and expresses the given polynomial in standard form?

8mn5 – 2m6 + 5m2n4 – m3n3 + n6 – 4m6 + 9m2n4 – mn5 – 4m3n3

n6 + 7mn5 + 14m2n4 – 5m3n3 – 6m6
–2m6 – 5m3n3 + 14m2n4 + 7mn5 + n6
14m2n4 + 7mn5 – 6m6 – 5m3n3 + n6
n6 – 6m6 + 7mn5 + 14m2n4 – 5m3n3

Answer 1

Combine like terms:

- m^6: -2m^6 - 4m^6 = -6m^6
- mn^5: 8mn^5 - mn^5 = 7mn^5
- m^2n^4: 5m^2n^4 + 9m^2n^4 = 14m^2n^4
- m^3n^3: -m^3n^3 - 4m^3n^3 = -5m^3n^3
- n^6: n^6

So the simplified polynomial is
n^6 + 7mn^5 + 14m^2n^4 - 5m^3n^3 - 6m^6,

which matches the first choice.