If it is a Student license trial that you have, then my understanding is that the answer is NO, a trial for that is not available for 32 bit Windows.
If you had purchased a Student license, then I am not certain as to whether you would be able to use a 32 bit Windows version or not. I have seen some hints that students might not have access to the necessary menu items.
If it were a Commercial / Professional license that was on Trial, or if it was an individual license within an Academic institution that was on Trial, then you would be able to ask Mathworks Sales for access to R2015b on trial basis. If I understand correctly, Mathworks will not provide that trial to users of Total Academic Headcount licenses; users would be expected to get the software from university staff.
If it were a Home license that was on Trial, then if I understand correctly, it is not possible to ask Mathworks to Trial R2015b or earlier; however, if I understand correctly, once a Home license has been purchased, it is possible to download and use the Windows 32 bit R2015b or earlier.
Research I did last year suggested to me that it is pretty likely that you can upgrade your laptop to 64 bit Windows, if it has been built any time in the last dozen years or so.
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