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

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

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

expand

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

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

Solution steps

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

Apply FOIL method:

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

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

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

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

Simplify

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

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

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

(2 x + 3 y = 1, 8) - (3 x + 2 y = 21)

- \frac{18}{( x + 1 ) ^{4}}

\frac{x ( x ^{2} + 4 x )}{5}

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