Please disregard first solution If adequate solution is post

Please disregard first solution. If adequate solution is posted you will get the 1350 points immediately.

Also please show work if possible

If H(s)=F(s)G(s) then

h(t)=L?1{F(s)G(s)}=?tu=0f(t?u)g(u)du

Here, I want to know if

H(s)=F(P(s))G(P(s))

h(t)=L?1s?t{F(P(s))G(P(s))}=L?1s?t{F(P(s))}?L?1s?t{G(P(s))}=?t0L?1s?t?u{F(P(s))}?L?1s?u{G(P(s))} du=?t0L?1s?u{F(P(s))}?L?1s?t?u{G(P(s))} du