Hong JeongHa's Tianyuanshu and

Tianyuanshu and Zengcheng Kaifangfa introduced in the Song–Yuan dynasties and their contribution to the theory of equations are one of the most important achievements in the history of Chinese mathematics. Furthermore, they became the most fundamental subject in the history of East Asian mathematics as well. The operations, or the mathematical structure of polynomials have been overlooked by traditional mathematics books. Investigation of GuIlJib ( 九一集) of Joseon mathematician Hong JeongHa reveals that Hong’s approach to polynomials is highly structural. For the expansion of ∏n=1 (x + ak), Hong invented a new method which we name Hong JeongHa’s synthetic expansion. Using this, he reveals that the processes in Zhengcheng Kaifangfa is not synthetic division but synthetic expansion.