Using Laplace Equations (I think)?

a. apply the definition of Laplace transform (the integral...). A little tedious but doable. Or, looking in your table, you have tⁿ f(t), which saves you many steps.

b. High School algebra: Rewrite as [steps left for you, partial fractions] 1/(s+3)² - 4/(s+3)³ + 10/(s+3)⁴.

Now, just look in your (inverse) laplace table for each of these. take note of the frequency shift one:

e^(ct)*f(t) becomes F(s-c).

Done!