The phenomenon of the scattering of sound by sound may be applied to audible sound reproduction in a predefined area, where two sound beams interact each other at an angle. Much effort has been carried out in this research area. However, it is rather time-consuming to obtain the scattered sound fields in the traditional way. Recently, the Gaussian-beam expansion technique, which was first proposed to achieve an analytical expression of the diffraction beam field from a circular piston, has been extended to analyze the scattered sound fields from two circular uniform pistons. However, this previous algorithm is related to the axisymmetric planar source, which is not applicable to the nonaxisymmetric case, like rectangular planar source. Therefore, this paper presents a simplified algorithm for calculating the difference frequency sound from two rectangular planar sources intersecting at small angles by applying the Gaussian-beam expansion technique to the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation. The two-dimensional integral expressions from the KZK equation for the primary sound fields of the displaced sound sources are simplified to analytical expressions and the multi-dimensional integral expression for the difference frequency sound is simplified to a one-dimensional integral using the Gaussian-beam expansion technique. As a result, the computation loading is significantly reduced. A detailed comparison between the difference frequency sound obtained from the two displaced circular pistons and two displaced rectangular planar sources is also carried out.