What is expand e^2x(e^4x-4e^{2x}) ?

The solution to expand e^2x(e^4x-4e^{2x}) is e^6x^2-4e^{2+2x}x

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expand e^2x(e^4x-4e^{2x})

expand

e^{2} x (e^{4} x - 4 e^{2 x})

e^{6} x^{2} - 4 e^{2 + 2 x} x

Solution steps

e^{2} x (e^{4} x - 4 e^{2 x})

Apply the distributive law:

a (b - c) = ab - a c

a = e^{2} x, b = e^{4} x, c = 4 e^{2 x}

= e^{2} x e^{4} x - e^{2} x \cdot 4 e^{2 x}

= e^{4} e^{2} xx - 4 e^{2} e^{2 x} x

Simplify

e^{4} e^{2} xx - 4 e^{2} e^{2 x} x : e^{6} x^{2} - 4 e^{2 + 2 x} x

= e^{6} x^{2} - 4 e^{2 + 2 x} x

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What is expand e^2x(e^4x-4e^{2x}) ?
The solution to expand e^2x(e^4x-4e^{2x}) is e^6x^2-4e^{2+2x}x