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

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

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

expand

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

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

Solution steps

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

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

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}

(- x + 1) (\frac{1}{2} x^{2} - 2 x + 1)

(- 1 + Δ x)^{3}

\frac{s + 1}{( s + 2 ) ( s + 3 )}

I n (\frac{y f}{x})

\frac{s - 1}{( s ^{2} - 2 s + 10 ) ( s + 2 )}

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