Homology group for trivial group action commutes with direct product in second coordinate

For two groups
Suppose $$G$$ is a group and $$A_1$$ and $$A_2$$ are (possibly isomorphic, possibly non-isomorphic) abelian groups. Let $$q$$ be a nonnegative integer. Denote by $$H_q(G;A_1)$$, $$H_q(G;A_2)$$, and $$H_q(G;A_1 \times A_2)$$ the homology groups for trivial group action of $$G$$ on $$A_1, A_2$$, and the external direct product $$A_1 \times A_2$$ respectively. Then, there is a canonical isomorphism:

$$H_q(G;A_1) \times H_q(G;A_2) \cong H_q(G;A_1 \times A_2)$$