This all follows directly from the definition of when a string matches a regular expression. You should consult the precise definition in your source; i'll go from memory. For example, suppose a string w matches (R + S)T. Then w = w_{1}w_{2}such that w_{1}matches R + S and w_{2}matches T. This in turn means that w_{1}matches either R or S. In the first case, w_{1}w_{2}matches RT, and in the second case, it matches ST; therefore, w = w_{1}w_{2}matches RT + ST. Other questions are similar.