The second cohomology group of module extensions banach algebras

We study on the second cohomology of the module extension Banach algebra A⊕1X, where A is a Banach algebra and X is a Banach A-bimodule. We characterize the defined 2-cocycles and 2-coboundaries on A⊕1X and as an interesting result we show that when H2(A,A)=0, then H2(A⊕1A,A⊕1A)=QM(A), where QM(A) is the set of quasi-multipliers on A. Also, we give some examples related to vanishing and nonvanishing of the second cohomology of various module extensions of Banach algebras.