regular expression problem $(A \cup B)^∗AB(A \cup B)^∗ \cup B^∗A^∗ = (A \cup B)^∗$

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can anybody prove the statement below using only basic identities? $A$ and $B$ are disjoint languages. $$(A \cup B)^∗AB(A \cup B)^∗ \cup B^∗A^∗ = (A \cup B)^∗$$