You permanently delete it by pressing on the icon until all of them start to wiggle, and then tapping on the little "x" in the upper left-hand corner. Also, make sure that you do not have the app set up in your computer to sync back, or it will.
You cannot do much more than "hide" purchased apps on the computer itself, but deleting by the "x" method does physically delete the app from your iPad, iPod, iPhone, etc.
As GB stated, you can use the "wiggle" and "x" method to remove the app from your iPad.
If you used iTunes from your computer to download and install the app on your iPad, you can delete the app from the computer by right-clicking (control-clicking) on the App within iTunes on your computer and selecting "Delete". This will remove the app from iTunes as well as the .ipa file in the Mobile Applications folder within ~/Music/iTunes/iTunes Media so that when you re-sync the device with your computer the app won't reinstall on your iPad.
That being said, the app will forever be associated with your Apple ID so that if you ever want to re-download the app it'll be available when you log in to the iTunes Store with your Apple ID.
Hope this helps!
This practice works for me. I have never used/set-up iCloud. When I delete unwanted apps the available storage on my iPad increases. My iCloud lists storage at 5.0 GB and available storage 5.0 GB - has no effect since it has never been used. I did know it was an old post, but I personally search posts for information regardless of date and often find useful information. I love your cat!