Generating Functions for (P1^r)(n) and (P2^r)(n)

In 1970 George E. Andrews defined the generating functions for (P1)^r(n) and (P2)^r(n). In this article these generating functions are discussed elaborately. This paper shows how to prove the theorem (P2)^r(n)=(P3)^r(n) with a numerical example when n= 9 and r= 2. In 1966 Andrews defined the terms A?(n) and B?(n), but this paper proves the remark A?(n)=B?(n) with the help of an example when n= 10. In 1961 N. Bourbaki defined the term P(n,m). This paper shows how to prove a Remark in terms of P(n,m), where P(n,m) is the number of partitions of the type of enumerated by (P3)^r(n) with the further restrictions that b1?2m.