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

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

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

expand

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

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

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

Simplify

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

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

\frac{2 ( 8 - 2 a )}{3}

\frac{3}{2 ( x - 4 ) ( x + 1 )}

2 (x - 3)^{2} + y^{2}

- \frac{1}{4 m} + \frac{1}{2 m}

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

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