What is expand-9/2 e^{4τ}(e^{-4t}-1) ?

The solution to expand-9/2 e^{4τ}(e^{-4t}-1) is -9/2 e^{4τ-4t}+9/2 e^{4τ}

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expand-9/2 e^{4τ}(e^{-4t}-1)

expand

- \frac{9}{2} e^{4 τ} (e^{- 4 t} - 1)

- \frac{9}{2} e^{4 τ - 4 t} + \frac{9}{2} e^{4 τ}

Solution steps

- \frac{9}{2} e^{4 τ} (e^{- 4 t} - 1)

Apply the distributive law:

a (b - c) = ab - a c

a = - \frac{9}{2} e^{4 τ}, b = e^{- 4 t}, c = 1

= - \frac{9}{2} e^{4 τ} e^{- 4 t} - (- \frac{9}{2} e^{4 τ}) \cdot 1

Apply minus-plus rules

- (- a) = a

= - \frac{9}{2} e^{4 τ} e^{- 4 t} + 1 \cdot \frac{9}{2} e^{4 τ}

Simplify

- \frac{9}{2} e^{4 τ} e^{- 4 t} + 1 \cdot \frac{9}{2} e^{4 τ} : - \frac{9}{2} e^{4 τ - 4 t} + \frac{9}{2} e^{4 τ}

= - \frac{9}{2} e^{4 τ - 4 t} + \frac{9}{2} e^{4 τ}

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What is expand-9/2 e^{4τ}(e^{-4t}-1) ?
The solution to expand-9/2 e^{4τ}(e^{-4t}-1) is -9/2 e^{4τ-4t}+9/2 e^{4τ}