Seem + to be + past participle

Dear teachers, 

Please tell me when we use 'to be + past participle' and when we use just an adjective after the verb 'seem'. 

For example, in the sentence The Prime Minister doesn't seem to be bothered with the plight of the sanitation workers in the city, can I just write/say The Prime Minister doesn't seem bothered with..." without having a change in the meaning? 

Another pair of sentences: 
- It seems good. 
- It seems to be good. 

Are both the sentences correct grammatically? Do they have the same meaning, please?