What is expand 0.5(e^{at}+e^{-at})u(t) ?

The solution to expand 0.5(e^{at}+e^{-at})u(t) is 0.5e^{at}tu+0.5e^{-at}tu

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expand 0.5(e^{at}+e^{-at})u(t)

expand

0.5 (e^{a t} + e^{- a t}) u (t)

0.5 e^{a t} t u + 0.5 e^{- a t} t u

Solution steps

0.5 (e^{a t} + e^{- a t}) u (t)

= 0.5 (t) u (e^{a t} + e^{- a t})

Apply the distributive law:

a (b + c) = ab + a c

a = 0.5 u (t), b = e^{a t}, c = e^{- a t}

= 0.5 u (t) e^{a t} + 0.5 u (t) e^{- a t}

= 0.5 e^{a t} (t) u + 0.5 e^{- a t} (t) u

Remove parentheses:

(a) = a

= 0.5 e^{a t} t u + 0.5 e^{- a t} t u

(x - 5) (x - i) (x + i)

\frac{1}{x ( x ^{3} - 1 )}

(x - 1) (2 + x + 3)

4 (2 - 1)

(\frac{x ^{3}}{4} - \frac{1}{x ^{3}})^{2}

What is expand 0.5(e^{at}+e^{-at})u(t) ?
The solution to expand 0.5(e^{at}+e^{-at})u(t) is 0.5e^{at}tu+0.5e^{-at}tu