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}

Apply minus-plus rules

+ (- a) = - a

= - 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{d}{d t} ((z (t, x, y)) (x^{2} y - y^{2}))

3 e^{x} tan (y) d x + (2 - e^{x}) sec^{2} (y) d y

A (3, - 2, 1) B (6, 1, - 2)

sec (\frac{π}{3} - \frac{π}{4})

\frac{x}{y ^{- 1}} (\frac{x}{y} - \frac{3 x ^{2}}{x y})

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