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

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

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

expand

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

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

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

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

= e^{4 x} e^{4 x} + e^{4 x} \cdot 4 x e^{4 x}

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

Simplify

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

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

e^{x} (- x^{2} + 7)

(x^{2} - x y) \frac{d y}{d x}

\frac{7 ( 373 - 7 )}{18}

x (x + y) d y - y^{2}

2 (x - 6 = - 3 (5 + x))

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