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Popular >

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

Solution

expand

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

Solution

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

Simplify

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

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Frequently Asked Questions (FAQ)

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