If the PS4 is configured as your brothers primary system then you should be able to play the game from other PSN accounts that are logged in to the same system.
Keep in mind that each PSN account can only have 1 primary PS4 and each PS4 can only have 1 primary PSN account. This means that if he is the primary then you can play his games on that PS4 but he could not play your games in the same PS4 unless he has also purchased the same game on his own account.