What is expand (e^t-1)^3e^{5t} ?

The solution to expand (e^t-1)^3e^{5t} is e^{8t}-3e^{7t}+3e^{6t}-e^{5t}

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expand (e^t-1)^3e^{5t}

expand

(e^{t} - 1)^{3} e^{5 t}

e^{8 t} - 3 e^{7 t} + 3 e^{6 t} - e^{5 t}

Solution steps

(e^{t} - 1)^{3} e^{5 t}

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

= e^{5 t} (3 e^{t} + e^{3 t} - 3 e^{2 t} - 1)

= e^{5 t} (e^{3 t} - 3 e^{2 t} + 3 e^{t} - 1)

Distribute parentheses

= e^{5 t} e^{3 t} + e^{5 t} (- 3 e^{2 t}) + e^{5 t} \cdot 3 e^{t} + e^{5 t} (- 1)

Apply minus-plus rules

+ (- a) = - a

= e^{5 t} e^{3 t} - 3 e^{5 t} e^{2 t} + 3 e^{t} e^{5 t} - 1 \cdot e^{5 t}

Simplify

e^{5 t} e^{3 t} - 3 e^{5 t} e^{2 t} + 3 e^{t} e^{5 t} - 1 \cdot e^{5 t} : e^{8 t} - 3 e^{7 t} + 3 e^{6 t} - e^{5 t}

= e^{8 t} - 3 e^{7 t} + 3 e^{6 t} - e^{5 t}

\frac{784000 ( - 2394 ln ( 21 ) + 33080 )}{ln ( 21 )}

\frac{4 + 2 s}{s \cdot ( s - 4 ) ( s - 1 )}

\frac{- x ^{2} - 2 x + 15}{( x - 1 ) ( x + 6 ) ( x + 3 )}

(x^{2} + x - 1)^{10}

\frac{( x - 1 ) y}{x}

What is expand (e^t-1)^3e^{5t} ?
The solution to expand (e^t-1)^3e^{5t} is e^{8t}-3e^{7t}+3e^{6t}-e^{5t}