What is expand e^{5x}(5xe^{5x}+e^{5x}) ?

The solution to expand e^{5x}(5xe^{5x}+e^{5x}) is 5e^{10x}x+e^{10x}

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expand e^{5x}(5xe^{5x}+e^{5x})

expand

e^{5 x} (5 x e^{5 x} + e^{5 x})

5 e^{10 x} x + e^{10 x}

Solution steps

e^{5 x} (5 x e^{5 x} + e^{5 x})

= e^{5 x} (5 e^{5 x} x + e^{5 x})

Apply the distributive law:

a (b + c) = ab + a c

a = e^{5 x}, b = 5 x e^{5 x}, c = e^{5 x}

= e^{5 x} \cdot 5 x e^{5 x} + e^{5 x} e^{5 x}

= 5 e^{5 x} e^{5 x} x + e^{5 x} e^{5 x}

Simplify

5 e^{5 x} e^{5 x} x + e^{5 x} e^{5 x} : 5 e^{10 x} x + e^{10 x}

= 5 e^{10 x} x + e^{10 x}

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What is expand e^{5x}(5xe^{5x}+e^{5x}) ?
The solution to expand e^{5x}(5xe^{5x}+e^{5x}) is 5e^{10x}x+e^{10x}