A friend of mine wants to know if you can play the expansion packs without their original CDs. As in install it and play it without the disc. She has Sims Deluxe Edition and is picking up expansion packs soon.

So the question, once the expansion packs (whichever they maybe) are installed, do you need the expansion pack disc to play the particular expansion?

You need the newest expansion you installed. You don't need the original or the older expansion disks.

so if she installs expansion pack ex. A, B, C and D, to play them all she would just need D, since it was the last one she installed?

Yes.