Yes. Use the first piece with the leads. Simply cut it to length as you stated. I wouldn't throw the remainder away though. Many places you could use it. You can certainly solder new leads to a cut end of a new strip. I used our leftover inside the island storage on a switch.
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2019 Montana HC 310RE
2010 Wildcat 29RLBS
2014 Ford F-350 Lariat 6.7
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