Mathematica vs Alpha output in Laplace transformation?

Questions
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1

I am learning my way around Mathematica. Using simple problems with known solutions I find that the output from Mathematica (V10) and alpha sometimes differ in the way they are presented, or rather Alpha provides more options.

For example computing the Laplace Transform, in Mathematica, of

LaplaceTransform[t^2 UnitStep[t - a], t, s]

yields

(E^(-a s) (2 E^(a s) UnitStep[-a] + 2 UnitStep[a] + 
   2 a s UnitStep[a] + a^2 s^2 UnitStep[a]))/s^3

while using Alpha returns alternate forms, including

Screenshotfrom2021-07-2017-59-57.png

How do I get Mathematica to output the alternate forms?

2

As it seems Wolfram|Alpha is assuming a>0. Try e.g.:

ltf = LaplaceTransform[t^2 UnitStep[t - a], t, s];
Refine[ltf, a > 0]
PiecewiseExpand[ltf]
3

Thanks. Refine works as hoped for. Using Expand, rather than PiecewiseExpand yields the same result.