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

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

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expand (1+e^{-x})^2

expand

(1 + e^{- x})^{2}

1 + 2 e^{- x} + e^{- 2 x}

Solution steps

(1 + e^{- x})^{2}

Apply Perfect Square Formula:

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

a = 1, b = e^{- x}

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

Simplify

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

= 1 + 2 e^{- x} + e^{- 2 x}

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

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

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

\frac{6 x ^{3} + 14 x ^{2} + x - 12}{x ( x - 1 ) ( x + 2 ) ^{2}}

\frac{1}{3} + \frac{2}{9} (1.1 - 1)

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