Resizing a VHD does not necessarily expand the partition on it

Today I was experimenting with dynamically expanding VHD (virtual hard disk) files. At one point, I decided I wanted to increase the maximum size of such a VHD, so I used the PowerShell Resize-VHD cmdlet. I then tried to put more things on the VHD, but Explorer informed me that there was insufficient space. Looking in Disk Management, I saw that the virtual drive had been expanded, but the partition on it was the same size as before. That makes sense, since volumes are not the same as drives. Fortunately, PowerShell also has a Resize-Partition cmdlet.