Yes you can use the logos of any Expedia Group brand on your website after you have successfully joined the respective program. Please make sure the logo is not tweaked in any way.
Help Center
https://help.affiliates.expediagroup.com/hc/en-us/articles/12407646780055-Your-guide-to-getting-started
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Getting started
Your guide to key things you need to know
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https://help.affiliates.expediagroup.com/hc/en-us/sections/13797161486103-Resources
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Research & insights
Discover affiliate strategies and insights
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https://help.affiliates.expediagroup.com/hc/en-us/articles/16773147563415
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Release notes
Learn about our latest updates and enhancements
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https://help.affiliates.expediagroup.com/hc/en-us/articles/18879025882391
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Drive your first booking
New to affiliate marketing? See our top tips to land that first booking
commission, links, payment