What is expand (2x+e^x)(x^2*e^x) ?

The solution to expand (2x+e^x)(x^2*e^x) is 2e^xx^3+e^{2x}x^2

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expand (2x+e^x)(x^2*e^x)

expand

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

2 e^{x} x^{3} + e^{2 x} x^{2}

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

Simplify

2 x (e^{x} x^{2}) + e^{x} (e^{x} x^{2}) : 2 e^{x} x^{3} + e^{2 x} x^{2}

= 2 e^{x} x^{3} + e^{2 x} x^{2}

\frac{0.1 ( - 2 s + 5 )}{s}

\frac{10 - 4 x}{x ( x - 2 )}

\frac{x + 7}{( x + 1 ) ( x ^{2} + 2 s + 2 )}

\frac{4 ( 5 n - 26 )}{5}

\frac{5 ( 16201 - 125 )}{18}

What is expand (2x+e^x)(x^2*e^x) ?
The solution to expand (2x+e^x)(x^2*e^x) is 2e^xx^3+e^{2x}x^2