Manipulating Laplace into form I need...

Hi all,

I've got something I need to take the laplace of, and it's in the form of

t^2 H(t-1)

I know to take advantage of the second shift theorem, I need to rearrange the left hand side so it has (t-1) in the t terms.

I also know that the final answer is

(t-1)^2 + 2(t-1) + 1, but I'm unsure of the method to consistently work through and get this solution.

From memory, it has to do with subbing in (t-1) into the t term, expanding out and doing balancing, but after mucking around for about 30 minutes I can't seem to get it out.

Can anyone please help with the process? Thank you.

P.s. Sorry for the non-latex math, I tried with it and am getting some weird errors.