Battery cable question

[Mister-B]

My battery died today. Had it tested, and it is bad, so I bought a new one. I noticed the battery terminals were a little corroded and banged up, so I bought new cables that have the terminals attached. Here's my question.... Both cables have that extra little smaller cable with the crimp at the end, but the original cables only had one of those. Should I just cut the smaller cable off the other side that doesn't need it?

I bought two if these:


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