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

The solution to expand (4e^{2x}+4xe^{2x})(2e^{2x})(x) is 8e^{4x}x+8e^{4x}x^2

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expand (4e^{2x}+4xe^{2x})(2e^{2x})(x)

expand

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

8 e^{4 x} x + 8 e^{4 x} x^{2}

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

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

= (2 e^{2 x}) (x) \cdot 4 e^{2 x} + (2 e^{2 x}) (x) \cdot 4 x e^{2 x}

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

Simplify

4 e^{2 x} (x) (2 e^{2 x}) + 4 e^{2 x} (x) x (2 e^{2 x}) : 8 e^{4 x} x + 8 e^{4 x} x^{2}

= 8 e^{4 x} x + 8 e^{4 x} x^{2}

\frac{1}{2 x ( 4 x - 50 )}

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

\frac{3 ( 2 + 1 )}{2}

\frac{d}{d p} ((x (p)) (20 (15 - p)))

(1 - t (x)) \cdot x^{'}

What is expand (4e^{2x}+4xe^{2x})(2e^{2x})(x) ?
The solution to expand (4e^{2x}+4xe^{2x})(2e^{2x})(x) is 8e^{4x}x+8e^{4x}x^2