The Laplace Transform of the expression (t-3)u2(t) - (t-2)u3(t) can be computed using the property that f(t-a)u(t-a) has a Laplace transform of the form e^(-as)F(s). Specifically, for the first term, the transform results in e^(-2s)F(s) where F(s) is the Laplace Transform of (t-3) evaluated at t=2. For the second term, the transform results in e^(-3s)F(s) where F(s) is the Laplace Transform of (t-2) evaluated at t=3. This approach effectively utilizes the unit step function to handle the shifts in the time domain.
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