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

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

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

expand

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

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

Solution steps

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

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

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

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

Apply minus-plus rules

+ (- a) = - a

= e^{x} e^{x} + 1 \cdot e^{x} - e^{x} e^{- x} - 1 \cdot e^{- x}

Simplify

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

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

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