What is expand (2e^{-4t}-2)^3 ?

The solution to expand (2e^{-4t}-2)^3 is 8e^{-12t}-24e^{-8t}+24e^{-4t}-8

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expand (2e^{-4t}-2)^3

expand

(2 e^{- 4 t} - 2)^{3}

8 e^{- 12 t} - 24 e^{- 8 t} + 24 e^{- 4 t} - 8

Solution steps

(2 e^{- 4 t} - 2)^{3}

Apply Perfect Cube Formula:

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

a = 2 e^{- 4 t}, b = 2

= (2 e^{- 4 t})^{3} - 3 (2 e^{- 4 t})^{2} \cdot 2 + 3 \cdot 2 e^{- 4 t} \cdot 2^{2} - 2^{3}

Simplify

(2 e^{- 4 t})^{3} - 3 (2 e^{- 4 t})^{2} \cdot 2 + 3 \cdot 2 e^{- 4 t} \cdot 2^{2} - 2^{3} : 8 e^{- 12 t} - 24 e^{- 8 t} + 24 e^{- 4 t} - 8

= 8 e^{- 12 t} - 24 e^{- 8 t} + 24 e^{- 4 t} - 8

4 (2 x^{5} + x^{4} - 2 x^{3} + 3)^{3}

(x + Δ x) (x - 2)

\frac{s + 3}{s ( s ^{2} + 1 )}

(- 2 e^{- 4 t} - 2)^{3}

\frac{( Y - ( ( X + 1 ) \cdot 4 ) )}{X}

What is expand (2e^{-4t}-2)^3 ?
The solution to expand (2e^{-4t}-2)^3 is 8e^{-12t}-24e^{-8t}+24e^{-4t}-8