What is expand e^x*(1+e^{-4x}) ?

The solution to expand e^x*(1+e^{-4x}) is e^x+e^{-3x}

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expand e^x*(1+e^{-4x})

expand

e^{x} \cdot (1 + e^{- 4 x})

e^{x} + e^{- 3 x}

Solution steps

e^{x} (1 + e^{- 4 x})

Apply the distributive law:

a (b + c) = ab + a c

a = e^{x}, b = 1, c = e^{- 4 x}

= e^{x} \cdot 1 + e^{x} e^{- 4 x}

= 1 \cdot e^{x} + e^{x} e^{- 4 x}

Simplify

1 \cdot e^{x} + e^{x} e^{- 4 x} : e^{x} + e^{- 3 x}

= e^{x} + e^{- 3 x}

\frac{( u - 5 ) ^{2}}{u}

2^{\frac{4}{3}}

3 (- 10 + 5)

2 (x + \frac{1}{3}) (x + \frac{1}{5}) (x + \frac{1}{4}) (x + \frac{1}{2})

(2 x^{3} y^{4} + 5 x) d x + (2 x^{m + 1} y^{n} + y^{3}) d y

What is expand e^x*(1+e^{-4x}) ?
The solution to expand e^x*(1+e^{-4x}) is e^x+e^{-3x}