Open facebook in your smartphone. At the top, there is a search bar. Everything you search there makes its prints in history. To clear the recent history, follow these steps:
Click on search bar, and you can see all your searches in the form of dropdown.
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There is a Edit button and you need to click on it. At the next page, you can see "Clear searches". Click on it to remove all the contents.
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Finally all your searches will be removed from facebook search.