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

x^{q (1 - q)}

y^{2} (y + 3 x \frac{d y}{d x})

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

- \frac{7 x ^{2}}{( x - 6 ) ( x + 7 )}

f (3, - 1)

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