What is expand (-x^2e^x)(2x-1) ?

The solution to expand (-x^2e^x)(2x-1) is -2e^xx^3+e^xx^2

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expand (-x^2e^x)(2x-1)

expand

(- x^{2} e^{x}) (2 x - 1)

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

Solution steps

(- x^{2} e^{x}) (2 x - 1)

= (- e^{x} x^{2}) (2 x - 1)

Apply the distributive law:

a (b - c) = ab - a c

a = (- x^{2} e^{x}), b = 2 x, c = 1

= (- x^{2} e^{x}) \cdot 2 x - (- x^{2} e^{x}) \cdot 1

= 2 x (- e^{x} x^{2}) - 1 \cdot (- e^{x} x^{2})

Simplify

2 x (- e^{x} x^{2}) - 1 \cdot (- e^{x} x^{2}) : - 2 e^{x} x^{3} + e^{x} x^{2}

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

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What is expand (-x^2e^x)(2x-1) ?
The solution to expand (-x^2e^x)(2x-1) is -2e^xx^3+e^xx^2