What is laplacetransform t^2-4t+4 ?

The answer to laplacetransform t^2-4t+4 is 2/(s^3)-4/(s^2)+4/s

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laplacetransform t^2-4t+4

laplace transform

t^{2} - 4 t + 4

\frac{2}{s ^{3}} - \frac{4}{s ^{2}} + \frac{4}{s}

Solution steps

L {t^{2} - 4 t + 4}

Use the linearity property of Laplace Transform:

For functions

f (t), g (t)

and constants

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= L {t^{2}} - 4 L {t} + L {4}

L {t^{2}} : \frac{2}{s ^{3}}

L {t} : \frac{1}{s ^{2}}

L {4} : \frac{4}{s}

= \frac{2}{s ^{3}} - 4 \cdot \frac{1}{s ^{2}} + \frac{4}{s}

Refine

\frac{2}{s ^{3}} - 4 \frac{1}{s ^{2}} + \frac{4}{s} : \frac{2}{s ^{3}} - \frac{4}{s ^{2}} + \frac{4}{s}

= \frac{2}{s ^{3}} - \frac{4}{s ^{2}} + \frac{4}{s}

What is laplacetransform t^2-4t+4 ?
The answer to laplacetransform t^2-4t+4 is 2/(s^3)-4/(s^2)+4/s