Question

8mn5-2m6+5m2n4-m3n3+n6-4m6+9m2n4-mn5-4m3n3 in standard form. I think i have it but want to make sure im teaching my child the right thing

Answer 1

Hello @parikhst ! Welcome to QuestionCove!

It would be best for us to write this problem with exponents clearly for it to be easier on the eyes

can you confirm that this is the problem we are working with?
\(8mn^5-2m^6+5m^2n^4-m^3n^3+n^6-4m^6+9m^2n^4-mn^5-4m^3n^3\)

Answer 2

yes it is. my answer is the standard form which i thought would be

n6-6m6+7mn5+14m2n4-5m3n3

sorry bout format

Answer 3

she asked why the n6 comes before the -6m6 because both exponents are 6

Answer 4

hmm
I do believe the values with m should come before n because of alphabetical order

but let me double check that real quick

Answer 5

thanks

Answer 6

i guess also, is that answer right? lol

Answer 7

now that im reading it may be a different answer where -6m6 is at the end

Answer 8

@AZ I could use some confirmation on this problem as well

I think you are making a good point with your latest comment

this problem is challenging because all of the values have the same "degree"

I believe the correct solution might be:
\(-6m^6 -5m^3n^3 +14m^2n^4 + 7mn^5 + n^6\)

Answer 9

http://tobybartels.name/MATH-0950/2008WN/standard/

Answer 10

so what i was thinkin is to swith the last and first so it would be n6....-6m6

Answer 11

im guessing you do positive numbers first and organize high to low and then go to negatives????

Answer 12

n6+7mn5+14m2n4-5m3n3-6m6

Answer 13

- the variables should be in alphabetical order when alone in each "term"
- if the terms have the same degree value, the leading variable should decrease in exponent with each term coming after it (m^6 comes before m^5n, which comes before m^4n^2, which comes before m^3 n^3

Answer 14

I don't think the coefficients play any role in the order of the terms (other than 0 being a bad coefficient to have)

Answer 15

I concur with @Angle 's answer. The the exponents of the first variable decrease as the second variable's exponents increase.

Answer 16

I agree with you @Angle

Convention is to have the terms in alphabetical order with the exponents counting down
The exponents for the m terms count down (6, 3, 2, 1, 0)

I suppose you could have the n exponents count down, but I've seen it mostly with the higher rank letter going for that role. It will depend on what the teacher wants.

Answer 17

so i get that. so is it because m comes before n the -6 is first term is first? if that the case im confused cause there is no option for starting with -6 int the multiple choice answer

Answer 18

ohh if there are multiple choice answers, please share

Answer 19

let me attach a file. she got it wrong and i don't want to give her the wrong answer cause they dont tell u the right one

Answer 20

We can also see that this calculator also simplifies it with -6m^6 at the front
https://www.wolframalpha.com/input/?i=8mn%5E5-2m%5E6%2B5m%5E2n%5E4-m%5E3n%5E3%2Bn%5E6-4m%5E6%2B9m%5E2n%5E4-mn%5E5-4m%5E3n%5E3

Answer 21

oh dear

ok, in this case we want it where the n^6 exponent is gradually decreasing

so n^6 followed by the term with the n^5, then n^4, then n^3

Answer 22

with the term that has no "n" value last

Answer 23

so im confused as to if its the first answer or the last

Answer 24

first answer

Answer 25

the -6m^6 comes last in this case

because we apparently want to have the n^6 be the leading variable

Answer 26

so is that standard where n descends first

Answer 27

correct

Answer 28

is there multiple ways of doing these types of problems?

Answer 29

You can think of \(-6m^6\) as \(-6m^6n^0\) because \(n^0 = 1\) assuming n is nonzero.

Answer 30

in this case, yes

but as jim mentioned, it seems to be teacher's preference at times like this

Answer 31

would it be ever based the highest exponent and whichever letter correscponds you descend with that first? or am i totally making that up. lets say there was an m8 would u descend w m's first

Answer 32

absolutely correct!

It is always first and foremost the highest degree value that comes first in standard form

Answer 33

last question promise! so would this be a correct answer as well

-6m6-5m3n3+14m2n4+7mn5+n6

Answer 34

kind of depends on your choices for the question

Answer 35

yes, that would be a correct answer as well

Answer 36

ok awesome thanks soooooo much you guys have been super helpful and i greatly appreciate it!

Answer 37

i would have given her the wrong answer and wrong info otherwise!

Answer 38

absolutely!

thanks for coming to questioncove to ask your question :)