Abstract: Bent functions are maximally nonlinear Boolean functions with an even number of variables. Not only for their own sake as interesting combinatorial objects, but also for their important applications in coding, cryptography and sequence design, bent functions have attracted a lot of attention in the last thirty years and there are rich results on constructions of them. In this talk, we propose new constructions of bent functions by adding the product of finitely many linear functions to known bent functions. In the cases these known bent functions are chosen to be Kasami functions, Gold-like functions and functionswith Niho exponents, respectively, three new explicit infinite families of bent functions are obtained. Computer experiments show that the proposed families also contain such bent functions attaining optimal algebraic degree. This work extends previous work of Mesnager and Xu et al. Keywords: Bent function, Kasami function, Gold-like function, Niho exponent, Walsh transform.