Dehn functions of higher rank arithmetic groups of type a_n in products of simple lie groups

Suppose G is an arithmetic group defined over a global field K, that the K-type of G is An with n at least 2, and that the ambient semisimple group that contains G as a lattice has at least two noncocompact factors. We use results from Bestvina-Eskin-Wortman and Cornulier-Tessera to show that G has a polynomially bounded Dehn function.