# Laplace Transform of Steps

So I'm trying to do the laplace transform of unit step functions. From the laplace table in my book it says :
$\mathcal{L}(u_c(t)f(t-c)) = e^{-cs}F(s)$

So my problem asks for the laplace transform of:
$tu_8(t)$

So should I did the following:
$(t-8)u_8(t) + 8u_8(t)$
$\mathcal{L}((t-8)u_8(t) + 8u_8(t)) = e^{-8s}F(s) +\frac{8e^{-8s}}{s}$

So I have two questions:
1.) Is my attempt to solve the problem correct or am I completely off?
2.) What will the F(s) be?

-

$$F(s)=\frac{1}{s^2}=\mathscr{L}\{t\}.$$ Everything else is OK.