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

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

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

expand

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

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

Solution steps

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

Apply FOIL method:

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

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

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

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

Simplify

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

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

\frac{( x + h ) ^{2} - 4 ( x + h )}{h}

6 (\frac{x + 2}{2})

\frac{e ^{- x}}{x ( x ^{2} - 3 x + 2 )}

(2 x^{2} - π x y^{3})^{2}

(3 y d x + 6 d x - x d y = 0) \frac{1}{x d y}

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