Hi Ian,
Marta here, from Trello Support.
Right now, while it's not possible to directly embed those videos, you could upload them as attachments to your cards.
You can add attachments from:
Here's an article with more information on adding attachments to your cards: http://help.trello.com/article/769-adding-attachments-to-cards
I hope that helps!
Cheers,
Marta
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