Instead, from your current, activated copy of Windows 7 or Windows 8.1, download the Windows 10 ISO file for the corresponding edition (Home or Pro), or create a bootable USB flash drive. Without exiting your current Windows version, double-click the ISO to mount it as a virtual DVD (or open the USB flash drive with installation media) and then double-click Setup.
Your goal is to get to the screen with the full range of options.
Choose the option that says you want to keep nothing. The Windows 10 Setup program installs a clean copy of the edition that corresponds to the one you have installed. As part of the process, it verifies the activation status of your old Windows, creates the new license certificate, and blows away your previous install. And you never had to enter a product key.
After you restart, your clean copy of Windows 10 is activated, and you can reinstall it any time without having to worry about activation. And you'll never need a product key again.