Editing Polynomial (section)

=== Addition and subtraction ===
Polynomials can be added using the [[associative law]] of addition (grouping all their terms together into a single sum), possibly followed by reordering (using the [[commutative law]]) and combining of like terms.<ref name="Edwards-1995-p47">{{cite book |last=Edwards |first=Harold M. |title=Linear Algebra |publisher=Springer |year=1995 |isbn=978-0-8176-3731-6 |page=47 |url=https://books.google.com/books?id=ylFR4h5BIDEC&pg=PA47}}</ref><ref>{{cite book |last=Salomon |first=David |title=Coding for Data and Computer Communications |publisher=Springer |year=2006 |isbn=978-0-387-23804-3 |page=459 |url=https://books.google.com/books?id=Zr9bjEpXKnIC&pg=PA459}}</ref> For example, if
<math display="block"> P = 3x^2 - 2x + 5xy - 2 </math> and <math display="block"> Q = -3x^2 + 3x + 4y^2 + 8</math>
then the sum
<math display="block">P + Q = 3x^2 - 2x + 5xy - 2 - 3x^2 + 3x + 4y^2 + 8 </math>
can be reordered and regrouped as
<math display="block">P + Q = (3x^2 - 3x^2) +  (- 2x + 3x) + 5xy + 4y^2 + (8 - 2) </math>
and then simplified to
<math display="block">P + Q = x + 5xy + 4y^2 + 6.</math>
When polynomials are added together, the result is another polynomial.<ref name=":0">{{Cite book|url=https://books.google.com/books?id=PagNAQAAIAAJ&q=the+addition+of+polynomials+is+an+operation+that+takes+any+two+polynomials+and+produce+always+another+polynomial,|title=Introduction to Algebra|date=1965|publisher=Yale University Press|pages=621|language=en|quote=Any two such polynomials can be added, subtracted, or multiplied. Furthermore, the result in each case is another polynomial}}</ref>

Subtraction of polynomials is similar.