What is expand e^x(-2(-e^{-x}x-e^{-x})) ?

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

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expand e^x(-2(-e^{-x}x-e^{-x}))

expand

e^{x} (- 2 (- e^{- x} x - e^{- x}))

2 x + 2

Solution steps

e^{x} (- 2 (- e^{- x} x - e^{- x}))

Remove parentheses:

(- a) = - a

= - e^{x} \cdot 2 (- e^{- x} x - e^{- x})

= - 2 e^{x} (- e^{- x} x - e^{- x})

Apply the distributive law:

a (b - c) = ab - a c

a = - e^{x} \cdot 2, b = - e^{- x} x, c = e^{- x}

= - e^{x} \cdot 2 (- e^{- x} x) - (- e^{x} \cdot 2) e^{- x}

Apply minus-plus rules

- (- a) = a

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

Simplify

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

= 2 x + 2

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

- 3 (x - 2 = 9 x + 16 - 4 x)

(x^{4} + y^{2}) d x + (2 x y + y^{3}) d y

e (x^{3} - x)^{8}

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