In this paper decomposition formulas and operator identities for second-order Gauss hypergeometric series of four variables in products of simpler known hypergeometric functions were obtained. The Choi - Hasanov method is used, based on inverse pairs of symbolic operators $$H\left(a,c\right)$$ and $$\overline{H}\left(a,c\right)$$  introduced in 2011 in the article of Junesang Choi, Anvar Hasanov «Applications of the operator $$H\left(a,c\right)$$ to the Humbert double hypergeometric functions». The obtained expansion formulas for hypergeometric functions of four variables will allow us to study the properties of these functions. By means of these expansions we can investigate the solvability of some boundary value problems for partial differential equations.