question about uninstalling and reinstalling

Why do you have to reinstall? If you're having troubles with your game, with corruption or some other issue, you don't need to uninstall the game and reinstall it. All you need to do is remove the "The Sims 3" folder from your My Documents directory and let the game generate a new one.

If you do have to reinstall because of other issues with your computer, you can still use your discs. Unless you have a 2009 copy of the base game, when you install the base game with the disc, it will connect to Origin to install, and Origin will run in the background when you reinstall everything else, but it won't be necessary to download anything else.

To uninstall correctly, you have to remove Sims 3 entries from the registry too. I think you need Registry Cleaner, or something like that. Someone else will have to explain that to you. Then, if you were installing only from discs, with Origin not running, you would have to re-enter your codes. But if you're connected to Origin, you may not need to do that. I don't have any experience with that myself, so I'm not sure. If you were downloading from Origin instead of using the discs, you definitely wouldn't have to enter the codes for each EP and SP. But even if you're reinstalling without going through Origin, if your content is registered with Origin, the codes are there, in your Origin account. Just open the information panel on whatever EP or SP you need the code for, and copy it from there.

Agreed... uninstalling/reinstalling can usually be avoided. What kind of issues are you having?

If you have all of your packs registered on Origin, you can download everything digitally through Origin. No codes required because they are tied to the account if indeed registered. How fast it downloads depends on internet speed. Installing by disc will require disc + codes unless the registry was not properly wiped after uninstalling which can cause problems. If you're going to uninstall, use the free version of CCleaner to clean registry.

Installing digitally through Origin will land you on patch 1.69. To stay on patch 1.67 will require base game copy printed before September 2012, all disc collection with codes, and 1.67 superpatch. The reason I'm mentioning patch levels is that some people don't like being tied to Origin with patch 1.69 as in it's required to run the game and you can not skip the launcher. If this doesn't bother you, installing the game digitally through Origin provided you have all packs registered already would be the easy route... All though slow internet connection will mean it takes longer to download.

thank you both

I agree with @SimplyJen about the steps to take if you plan on reinstalling with your discs. There is one extra step you should consider before using this method of reinstalling and that is to do with updating the launcher. I would suggest reading this link first which explains it better than I can.
https://forums.thesims.com/en_US/discussion/935445/patch-install-status-as-of-dec-2017-store-patch-download-removed#latest

Having a lot of store content I would have come to grief without this from @TOLKIEN and further help and guidance from @igazor.