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

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

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

expand

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

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

Solution steps

(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 e^{2 x} x

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

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

Simplify

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