What is expand e^t(-e^{-t}+1) ?

The solution to expand e^t(-e^{-t}+1) is -1+e^t

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expand e^t(-e^{-t}+1)

expand

e^{t} (- e^{- t} + 1)

- 1 + e^{t}

Solution steps

e^{t} (- e^{- t} + 1)

Apply the distributive law:

a (b + c) = ab + a c

a = e^{t}, b = - e^{- t}, c = 1

= e^{t} (- e^{- t}) + e^{t} \cdot 1

Apply minus-plus rules

+ (- a) = - a

= - e^{t} e^{- t} + 1 \cdot e^{t}

Simplify

- e^{t} e^{- t} + 1 \cdot e^{t} : - 1 + e^{t}

= - 1 + e^{t}

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