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May 19th, 2015, 07:00 PM   #1
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The letters in a polynomial's standard form

Is it only the degree that matters and not alphabetical order or anything? In many examples I'm finding, the answers seem to have the variables swapped to be alphabetical (x always before y and 2x before 6y), but I can't seem to find anything clarifying if it's necessary. (Sorry if you find something by Googling in less than a minute; I've been looking for about seven minutes myself, looking through different pages through about four websites, but I know I don't always have the best Googling technique.)

Edit: Mostly I'm wondering if it would be okay to have $\displaystyle y^4$ before $\displaystyle x^4$ or similar, or if there's something improper about that.
Edit 2: For a concrete example: Would $\displaystyle 4x^{2}y + 9y^{2}x$ be as acceptable as $\displaystyle 9y^{2}x + 4x^{2}y$, since both terms are to the second power?

Last edited by Rexan; May 19th, 2015 at 07:11 PM.
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May 19th, 2015, 07:27 PM   #2
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By convention, variables are usually listed in alphabetical order and it's usually best to adhere
to convention, unless you have a good reason not to, e.g. to emphasise something or to
enhance the latter stages of a calculation.

I'd write your example as $\displaystyle 4x^2y+9xy^2$ (which may also be written as $\displaystyle xy(4x+9y)$).
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