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

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

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

expand

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

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

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

Simplify

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

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

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