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{3}{x ( x ^{2} + 3 )}

6 x - 4 (2 x + 1 = 12)

(5 a + b = 5,) - (3 a + b = 4)

(3 e + 5) (3 e - 5)

15 (3 x - 1) - 7 (x - 1 = 2 (1 + 9 x))

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