An approach is presented to get matrix representations for classical a
nd more general r-Bezoutians with entries from a noncommutative ring.
Formulas due to Ammar and Gader, Barnett, Gohberg and Semencul, Gohber
g and Heinig, Kravitsky and Russakovskii, Lerer and Tismentsky, Ptak,
and Wimmer, as well as some generalizations and modifications, are obt
ained in a unified way.