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How to manage deleted files on a Chromebook
Drop your ChromeOS files in the trash when you’re done with them.
And note that there’s no syncing between the trash folder for local files on your Chromebook and that on Google Drive — these are separate spaces. If you want to erase or recover them before the end of the 30-day window, follow the Trash link on the Google Drive navigation pane. To delete a file, select it then either click the trash icon at the top right, or press Launcher+Backspace( Alt-Shift-Backspace also works).
Or read this on The Verge