Strong one-dimensional Hardy-type inequalities with additional terms

New one-dimensional Hardy-type inequalities with additional terms are proved. Weight functions of inequalities include positive and negative powers of x and (2-x). In some cases, the constants in the resulting one-dimensional inequalities are sharp. One-dimensional inequalities with additional terms are used to justify multidimensional inequalities, with weight functions depending on the powers of the Davis distance or the distance function to the boundary of domain.