Searching for a for Need for Speed: Hot Pursuit (2010)
If you cannot find a 2010 key, buy on Steam or EA App. It costs roughly $30 (often on sale for $10).
No algorithm can generate a valid EA product key offline because EA uses a server-side checksum. The only functional "cracks" bypass the key request entirely, but discussing them violates many platform policies. Your best bet remains the legal routes above.
This article is for educational purposes. Using cracked software or keygens is illegal and dangerous. Always purchase software directly from authorized retailers.
Assuming you have a verified, unused product key: