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

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

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

expand

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

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

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

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

Simplify

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

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

3250 + 5160

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\frac{45 ( n + 1 )}{2 n}

- \frac{10 ( 1985 - 5 )}{49}

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