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

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

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

expand

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

1 - e^{- 2 x}

Solution steps

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

Apply Difference of Two Squares Formula:

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

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

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

Simplify

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

= 1 - e^{- 2 x}

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