The Golod property for products and high symbolic powers of monomial ideals

We show that for any two proper monomial ideals I and J   in the polynomial ring S=K[x1,…,xn]S=K[x1,…,xn] the ring S/IJS/IJ is Golod. We also show that if I is squarefree then for large enough k   the quotient S/I(k)S/I(k) of S by the kth symbolic power of I is Golod. As an application we prove that the multiplication on the cohomology algebra of some classes of moment-angle complexes is trivial.