What is te^{-t}u(t)*e^{-t}u ?

The solution to te^{-t}u(t)*e^{-t}u is e^{-2t}t^2u^2

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simplify te^{-t}u(t)*e^{-t}u

simplify

t e^{- t} u (t) \cdot e^{- t} u

e^{- 2 t} t^{2} u^{2}

Solution steps

t e^{- t} u (t) e^{- t} u

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{- t} e^{- t} = e^{- t - t}

= t u t e^{- t - t} u

Add similar elements:

- t - t = - 2 t

= t u t e^{- 2 t} u

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

tt = t^{1 + 1}

= u t^{1 + 1} e^{- 2 t} u

Add the numbers:

1 + 1 = 2

= u t^{2} e^{- 2 t} u

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

uu = u^{1 + 1}

= t^{2} e^{- 2 t} u^{1 + 1}

Add the numbers:

1 + 1 = 2

= t^{2} e^{- 2 t} u^{2}

4.62 \cdot 1 0^{- 2}

(1.6 m^{3} n) (0.8 m^{2} n^{3})

5 e^{- 1.612}

(4 x - 8) e^{- 5 x}

280 m x^{2} y^{2}

What is te^{-t}u(t)*e^{-t}u ?
The solution to te^{-t}u(t)*e^{-t}u is e^{-2t}t^2u^2