What is laplacetransform t-(t-5)(-(t-5)) ?

The answer to laplacetransform t-(t-5)(-(t-5)) is 2/(s^3)-9/(s^2)+(25)/s

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laplacetransform t-(t-5)(-(t-5))

laplace transform

t - (t - 5) (- (t - 5))

\frac{2}{s ^{3}} - \frac{9}{s ^{2}} + \frac{25}{s}

Solution steps

L {t - (t - 5) (- (t - 5))}

Expand

t - (t - 5) (- (t - 5)) : t^{2} - 9 t + 25

= L {t^{2} - 9 t + 25}

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}} - 9 L {t} + L {25}

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

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

L {25} : \frac{25}{s}

= \frac{2}{s ^{3}} - 9 \cdot \frac{1}{s ^{2}} + \frac{25}{s}

Refine

\frac{2}{s ^{3}} - 9 \frac{1}{s ^{2}} + \frac{25}{s} : \frac{2}{s ^{3}} - \frac{9}{s ^{2}} + \frac{25}{s}

= \frac{2}{s ^{3}} - \frac{9}{s ^{2}} + \frac{25}{s}

f (x) = 2 x^{2} - 7, at x = - 2

4 x + y^{2} = 13, x = 3 y

(ln (3 x))^{^{'}}

6 e^{- 5 t} + 5 t

\frac{\partial}{\partial x} ((x^{2} + y) (x - y^{2}))

What is laplacetransform t-(t-5)(-(t-5)) ?
The answer to laplacetransform t-(t-5)(-(t-5)) is 2/(s^3)-9/(s^2)+(25)/s