When deleting an AD object, it will (if the Recycle bin is enabled) be moved to the Active Directory recycle bin.
Sometimes you want to permamently remove the object, for example if you want to recreate a pc or server with the same name.
To do this, open PowerShell and type in the following commands;
To get the object your are looking for;
Get-ADObject -Filter 'isDeleted -eq $True -and Name -like "objectname*"' -IncludeDeletedObjects
Example;
Get-ADObject -Filter 'isDeleted -eq $True -and Name -like "PC-01234*"' -IncludeDeletedObjects
To delete the object;
Get-ADObject -Filter 'isDeleted -eq $True -and Name -like "PC-01234*"' -IncludeDeletedObjects | Remove-ADOjbect