Which polynomial correctly combines the like terms and expresses the given polynomial in standard form? 8mn5-2m6+5m2n4-m3n3+n6-4m6+9m2n4-mn 5-4m3n3

The answer would be 7mn^5 - 2m^6 + 14m^2n^4 - 5m^3n^3 + n^6

Step-by-step explanation:

In order to find that answer, start by grouping all of the terms by their variable values. Ones that are the same should be combined.

8mn^5 - mn^5 = 7mn^5

2m^6 - 4m^6 = -2m^6

5m^2n^4 + 9m^2n^4 = 14m^2n^4

-m^3n^3 - 4m^3n^3 = -5m^3n^3

n^6 = n^6

Now we simply combine them all to get

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

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for