We know that distributive law on left holds for ordinals, i.e. for every ordinals $\alpha, \beta, and \gamma$ we have: $\alpha.(\beta+\gamma)=\alpha.\beta+ \alpha. \gamma$, I know there is no law on right in general. My question is: if $\beta$ is a natural number and $\gamma$ is a limit ordinal, I heard that we have $(\alpha+\beta).\gamma= \alpha. \gamma$, How is its proof?
Thank you for your time and help.