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

The solution to expand (-e^{2t}-2e^{-t})^3 is -e^{6t}-6e^{3t}-12-8e^{-3t}

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

expand

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

- e^{6 t} - 6 e^{3 t} - 12 - 8 e^{- 3 t}

Solution steps

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

Apply Perfect Cube Formula:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

a = - e^{2 t}, b = 2 e^{- t}

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

Simplify

(- e^{2 t})^{3} - 3 (- e^{2 t})^{2} \cdot 2 e^{- t} + 3 (- e^{2 t}) (2 e^{- t})^{2} - (2 e^{- t})^{3} : - e^{6 t} - 6 e^{3 t} - 12 - 8 e^{- 3 t}

= - e^{6 t} - 6 e^{3 t} - 12 - 8 e^{- 3 t}

(3 x^{2} - 1) e^{x} + e^{x} (x^{3} - x)

\frac{1}{( 2 ( x + 2 ) )}

\frac{( 1 + ( x + 3 ) ( x + 2 ) )}{( x + 3 )}

0.00289867 (e^{- 2.40187 t} - e^{- 26.0214 t})

\frac{2 ( x - 3 )}{3}

What is expand (-e^{2t}-2e^{-t})^3 ?
The solution to expand (-e^{2t}-2e^{-t})^3 is -e^{6t}-6e^{3t}-12-8e^{-3t}