What is expand (1-e^{-2s})^2 ?

The solution to expand (1-e^{-2s})^2 is 1-2e^{-2s}+e^{-4s}

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expand (1-e^{-2s})^2

expand

(1 - e^{- 2 s})^{2}

1 - 2 e^{- 2 s} + e^{- 4 s}

Solution steps

(1 - e^{- 2 s})^{2}

Apply Perfect Square Formula:

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

a = 1, b = e^{- 2 s}

= 1^{2} - 2 \cdot 1 \cdot e^{- 2 s} + (e^{- 2 s})^{2}

Simplify

1^{2} - 2 \cdot 1 \cdot e^{- 2 s} + (e^{- 2 s})^{2} : 1 - 2 e^{- 2 s} + e^{- 4 s}

= 1 - 2 e^{- 2 s} + e^{- 4 s}

\frac{x ^{m + 1} ( - x m - x + m + 2 )}{( m + 1 ) ( m + 2 )}

\frac{( x - 3 ) \cdot ( x - 5 ) \cdot ( x - 7 )}{48}

\frac{5 x ^{2} + 60 x - 5}{( x + 1 ) ( x - 4 ) ( x + 5 )}

e^{2 - t} U (t - 1)

\frac{5}{( s + 1 ) ^{3}}

What is expand (1-e^{-2s})^2 ?
The solution to expand (1-e^{-2s})^2 is 1-2e^{-2s}+e^{-4s}