What is expand (1-e^{-x/8})^3 ?

The solution to expand (1-e^{-x/8})^3 is 1-3e^{-x/8}+3e^{-x/4}-e^{-(3x)/8}

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expand (1-e^{-x/8})^3

expand

(1 - e^{- \frac{x}{8}})^{3}

1 - 3 e^{- \frac{x}{8}} + 3 e^{- \frac{x}{4}} - e^{- \frac{3 x}{8}}

Solution steps

(1 - e^{- \frac{x}{8}})^{3}

Apply Perfect Cube Formula:

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

a = 1, b = e^{- \frac{x}{8}}

= 1^{3} - 3 \cdot 1^{2} e^{- \frac{x}{8}} + 3 \cdot 1 \cdot (e^{- \frac{x}{8}})^{2} - (e^{- \frac{x}{8}})^{3}

Simplify

1^{3} - 3 \cdot 1^{2} e^{- \frac{x}{8}} + 3 \cdot 1 \cdot (e^{- \frac{x}{8}})^{2} - (e^{- \frac{x}{8}})^{3} : 1 - 3 e^{- \frac{x}{8}} + 3 e^{- \frac{x}{4}} - e^{- \frac{3 x}{8}}

= 1 - 3 e^{- \frac{x}{8}} + 3 e^{- \frac{x}{4}} - e^{- \frac{3 x}{8}}

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What is expand (1-e^{-x/8})^3 ?
The solution to expand (1-e^{-x/8})^3 is 1-3e^{-x/8}+3e^{-x/4}-e^{-(3x)/8}