@Neethling7 The laptop you've listed would probably run the base game, on low settings, and any stuff pack you'd like. But it's not going to be able to handle Pets, Seasons, or Island Paradise, and probably not Showtime either. Whether it could run World Adventures and Late Night would be a close call, even on the lowest settings, but I wouldn't recommend it—you could end up overheating and damaging the computer. In fact, even the base game would put more stress on the hardware than it's designed to take, especially over the long term.
Laptops that can run all TS3 packs on high settings are usually $900 U.S. and up, although I can often find one for under $800. Prices will be higher in other countries, although how much depends on the country. I could look for better options for you, but there won't be anything in the price range of the HP. If you're interested, just list your budget and country, as well as anything else you'd like to do with the laptop, like other games or apps you want to run.