Question 1151789
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Standard form in this case is alphabetical ordering.


It means that the outer ordering must go in descending order of total degrees of monomials.


Inside the set of monomials of the same degree, the ordering should go in alphabetical ordering. 
It means descending order for variable x and ascending order for variable y.


The opposite ordering is also admitted.


But, in any case, if you talk about the standard form, you should select on EITHER direct alphabetic ordering 

OR <U>opposite</U> to the alphabetic ordering, but only ONE of the two.


Mixing two different orderings in one expression is not allowed in standard form.


In this sense, ordering by Marcus is <U>CONSISTENT</U>;  the ordering by Ariel <U>is not consistent</U>.
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Edwin, thanks for asking.



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Surely, the average school Math student will not understand the reason, why this issue is discussed, at all.


It can be important for them, for example, when some problem asks them to write 24-th term of the binomial expansion of  {{{(x+y)^37}}}.


In Math, some standard ordering is also used sometimes, for example, for classification of surfaces in multi-dimensional spaces,

or when Fourier or Laplace transformations are performed on differential operators in multi-dimensional spaces,

but these subjects are far above of understanding of school students.


So, my opinion is that it is better for student to solve 25 other problems than to think / (to spend) long time on this one.