<P> Formula (1) is valid more generally for any elements x and y of a semiring satisfying xy = yx . The theorem is true even more generally: alternativity suffices in place of associativity . </P> <P> The binomial theorem can be stated by saying that the polynomial sequence (1, x, x, x, ...) is of binomial type . </P> <Ul> <Li> The binomial theorem is mentioned in the Major - General's Song in the comic opera The Pirates of Penzance . </Li> <Li> Professor Moriarty is described by Sherlock Holmes as having written a treatise on the binomial theorem . </Li> <Li> The Portuguese poet Fernando Pessoa, using the heteronym Álvaro de Campos, wrote that "Newton's Binomial is as beautiful as the Venus de Milo . The truth is that few people notice it ." </Li> <Li> In the 2014 film The Imitation Game, Alan Turing makes reference to Issac Newton's work on the Binomial Theorem during his first meeting with Commander Denniston at Bletchley Park . </Li> </Ul> <Li> The binomial theorem is mentioned in the Major - General's Song in the comic opera The Pirates of Penzance . </Li>

Describe the pattern on the exponents on x in the expansion of (x + y)n