I have the question $\mathscr{L}((t-2)^2u_2(t))(s)$.
I was wondering why I couldn't substitute $t-2$ for $\eta$ as $u_2(t)$ could be rewritten as $u_0(t-2)$ so it could fulfill the transform $\mathscr{L}(u_c(t)f(t-c))(s)=e^{-cs}F(s)$. If I had done this substitution the $e^{-cs}$ term would become $0$.
Furthermore, how would one solve this problem?