What is expand e^{3t}e^{-t}(2e^t-1) ?

The solution to expand e^{3t}e^{-t}(2e^t-1) is e^{2t}(2e^t-1)

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expand e^{3t}e^{-t}(2e^t-1)

expand

e^{3 t} e^{- t} (2 e^{t} - 1)

e^{2 t} (2 e^{t} - 1)

Solution steps

e^{3 t} e^{- t} (2 e^{t} - 1)

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= e^{3 t} \frac{1}{e ^{t}} (2 e^{t} - 1)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot e ^{3 t} ( 2 e ^{t} - 1 )}{e ^{t}}

Multiply:

1 \cdot e^{3 t} = e^{3 t}

= \frac{e ^{3 t} ( 2 e ^{t} - 1 )}{e ^{t}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{e ^{3 t}}{e ^{t}} = e^{3 t - t} = e^{2 t}

= e^{2 t} (2 e^{t} - 1)

(2 e^{2 x} - 2) e^{- 2 x}

3.25 \cdot 1 0^{- 9}

\frac{5}{7 x}

What is expand e^{3t}e^{-t}(2e^t-1) ?
The solution to expand e^{3t}e^{-t}(2e^t-1) is e^{2t}(2e^t-1)