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

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

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

expand

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

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

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

Apply minus-plus rules

+ (- a) = - a

= 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}

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

4 x + 3 (x - 2 = 18 - x)

x cos (x) d x + (1 - 6 y) d y

\frac{d}{d y} ((x) (2 x - 1))

(x^{2} - 1) ln (3)

\frac{( x - 5 ) ^{2}}{3}

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