While I couldn't find any information on a free product key for MathType 7.4.4.516, there are some free alternatives and options available:
Academic Discounts: Students and teachers can often purchase MathType at a significantly reduced price through their institution or the official Wiris website.
If you decide to continue using the software after the trial, legitimate licenses are available through the WIRIS Store :
If you need the advanced templates, seamless Office integration, and dedicated support that MathType offers, the safest and most sustainable path is to or leverage an academic discount . For occasional or budget‑constrained work, one of the free tools listed above can often meet the same needs without legal or security concerns.
that provides access to all features, including the AI-powered handwriting tool and seamless integration with Microsoft Office and Google Workspace. Academic Discounts