A formla of obtaining the number of polynimial expansion combined terms based on the "Yanghui triangle"

Abstract

The history of ancient Chinese mathematics once had its own brilliant chapter, and the discovery of Yanghui Triangle is a very wonderful page. The Yanghui Triangle was discovered by the ancient Chinese mathematician Jia Xian in the 11th century and quoted by the mathematician Yang Hui in his book of the Southern Song Dynasty, so that we can understand Jia Xian's great contribution to mathematics today. "Yanghui Triangle" has always been a very interesting part of middle school mathematics learning. Through training students' understanding of "Yanghui Triangle", students can have stronger thinking ability of combination of number and form. This paper breaks away from the traditional research content of the coefficients of "Yanghui triangle", innovatively studies the relationship between Yanghui triangle and polynomial expansions, and proposes a method to quickly determine the final number of polynomial expansions under different powers.