Editing Binomial theorem (section)

== In abstract algebra ==

The binomial theorem is valid more generally for two elements {{math|''x''}} and {{math|''y''}} in a [[Ring_(mathematics)|ring]], or even a [[semiring]], provided that {{math|1=''xy'' = ''yx''}}.  For example, it holds for two {{math|''n'' × ''n''}} matrices, provided that those matrices commute; this is useful in computing powers of a matrix.<ref>{{cite book |last=Artin |first=Michael |author-link=Michael Artin |title=Algebra |edition=2nd |year=2011 |publisher=Pearson |at=equation (4.7.11)}}</ref>

The binomial theorem can be stated by saying that the [[polynomial sequence]]  {{math|1={{mset|1, ''x'', ''x''<sup>2</sup>, ''x''<sup>3</sup>, ...}}}} is of [[binomial type]].