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

The solution to expand (e^{2x})(2xe^{2x}+e^{2x}) is 2e^{4x}x+e^{4x}

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expand (e^{2x})(2xe^{2x}+e^{2x})

expand

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

2 e^{4 x} x + e^{4 x}

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

a = (e^{2 x}), b = 2 x e^{2 x}, c = e^{2 x}

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

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

Simplify

2 e^{2 x} x (e^{2 x}) + e^{2 x} (e^{2 x}) : 2 e^{4 x} x + e^{4 x}

= 2 e^{4 x} x + e^{4 x}

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What is expand (e^{2x})(2xe^{2x}+e^{2x}) ?
The solution to expand (e^{2x})(2xe^{2x}+e^{2x}) is 2e^{4x}x+e^{4x}