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

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

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

expand

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

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

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

Simplify

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

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

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