# Determine the Laplace transform of the given function f. f(t)=(t -1)^2 u_2(t)

Determine the Laplace transform of the given function f.
$f\left(t\right)=\left(t-1{\right)}^{2}{u}_{2}\left(t\right)$
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Step 1
Here laplace transform of given function is to be calculated.
Given function is $f\left(t\right)=\left(t-1{\right)}^{2}{u}_{2}\left(t\right)$
So expand the function as follows,
$f\left(t\right)={t}^{2}u\left(t\right)+u\left(t\right)-2tu\left(t\right)$
Take Laplace of the function f(t)
Step 2
Then,
$L\left(f\left(t\right)\right)=L\left({t}^{2}u\left(t\right)+u\left(t\right)-2tu\left(t\right)\right)$
$=\frac{2}{{s}^{3}}+\frac{1}{s}-\frac{2}{{s}^{2}}$
Hence the Laplace Transform of the