Just to be sure about your intentions:
You want to obtain LED strips similar to those shown on the Alienware 18 laptop and mount/glue/sticky those strips to your laptop - Correct?
What make and model laptop do you have? Does your laptop even support RGB internally or via a laptop USB port?
Are you comfortable opening up the laptop and making internal connections that, somehow need to be routed out to the visible strips?
Attaching the strips to the case may likewise be problematic.
Overall, full disclosure, I have some concerns about the concept in general.
Work out more of the details about what you wish to do and post accordingly.
Before doing anything.
My concern is that there may unforeseen and irreversible consequences.