1
Look at the function keys (F1 - F12) on your keyboard, if one of those keys has a touchpad symbol with a line through it, try pressing that key or Fn + that key to disable the touchpad.
2
If none of those keys has that symbol, open the old Control Panel.
At the top of the old Control Panel, set view to large icons.
Open the Mouse applet in the old Control Panel.
Check if there is a tab on that utility specifically for the Synaptics or Elan touchpad, if so, check on that tab to see if HP provided an option to disable the touchpad.
Or check each tab for an option to disable the touchpad when a mouse is connected.
3
If none of those options resolve the problem, right click your Start Button and open Device Manager.
Expand the 'Mice and other pointing Devices' section.
If you see a Synaptics or Elan touchpad listed in there, right click it and select Disable, do not uninstall it, because Windows would reload the driver automatically.