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

The solution to expand e^{2x}*2(e^x+e^{-x}) is 2e^{3x}+2e^x

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

expand

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

2 e^{3 x} + 2 e^{x}

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

Simplify

2 e^{x} e^{2 x} + 2 e^{2 x} e^{- x} : 2 e^{3 x} + 2 e^{x}

= 2 e^{3 x} + 2 e^{x}

\frac{( x + Δ x ) ^{3}}{Δ x}

\frac{( - 2 x + 4 ) ^{7}}{( 3 x - 5 ) ^{5}}

x d y - 4 (y + x^{6}) d x

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(6 x + 5) (\frac{1}{2} e^{2 x})

What is expand e^{2x}*2(e^x+e^{-x}) ?
The solution to expand e^{2x}*2(e^x+e^{-x}) is 2e^{3x}+2e^x