The Laplace transform of the function (t − 1)^2u(t − 1) is derived using the formula L{f(t-a)u(t-a)}(s) = e^-as F(s). In this case, f(t) is identified as t^2, which is crucial for applying the transform correctly. The confusion arises from the interpretation of the function's argument; while (t-1)^2 is the expression, the function f(t) itself is defined as t^2. This distinction is essential for accurate computation of the Laplace transform.
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