What is expand (2-e^{-7x})^3 ?

The solution to expand (2-e^{-7x})^3 is 8-12e^{-7x}+6e^{-14x}-e^{-21x}

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expand (2-e^{-7x})^3

expand

(2 - e^{- 7 x})^{3}

8 - 12 e^{- 7 x} + 6 e^{- 14 x} - e^{- 21 x}

Solution steps

(2 - e^{- 7 x})^{3}

Apply Perfect Cube Formula:

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

a = 2, b = e^{- 7 x}

= 2^{3} - 3 \cdot 2^{2} e^{- 7 x} + 3 \cdot 2 (e^{- 7 x})^{2} - (e^{- 7 x})^{3}

Simplify

2^{3} - 3 \cdot 2^{2} e^{- 7 x} + 3 \cdot 2 (e^{- 7 x})^{2} - (e^{- 7 x})^{3} : 8 - 12 e^{- 7 x} + 6 e^{- 14 x} - e^{- 21 x}

= 8 - 12 e^{- 7 x} + 6 e^{- 14 x} - e^{- 21 x}

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What is expand (2-e^{-7x})^3 ?
The solution to expand (2-e^{-7x})^3 is 8-12e^{-7x}+6e^{-14x}-e^{-21x}