Pawnoffer in middlegame - to get and use an open file

Pawn offers are in middle game a strategic weapon, for example to open a file and use it for a rook. Let us look first at an easy example:

1. Black offers a pawn white should better not accept

In that example black would have got for that offered pawn a open b-file and could have used it immediately. White was wise and neglected the pawn offer with Bd3.

Let us come to the second example:

 2.  white offers a pawn to get control of the d-file