What is expand (-(x^3)/3-(x^2)/2)e^{2x} ?

The solution to expand (-(x^3)/3-(x^2)/2)e^{2x} is -(e^{2x}x^3)/3-(e^{2x}x^2)/2

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expand (-(x^3)/3-(x^2)/2)e^{2x}

expand

(- \frac{x ^{3}}{3} - \frac{x ^{2}}{2}) e^{2 x}

- \frac{e ^{2 x} x ^{3}}{3} - \frac{e ^{2 x} x ^{2}}{2}

Solution steps

(- \frac{x ^{3}}{3} - \frac{x ^{2}}{2}) e^{2 x}

= e^{2 x} (- \frac{x ^{3}}{3} - \frac{x ^{2}}{2})

Apply the distributive law:

a (b - c) = ab - a c

a = e^{2 x}, b = - \frac{x ^{3}}{3}, c = \frac{x ^{2}}{2}

= e^{2 x} (- \frac{x ^{3}}{3}) - e^{2 x} \frac{x ^{2}}{2}

Apply minus-plus rules

+ (- a) = - a

= - e^{2 x} \frac{x ^{3}}{3} - e^{2 x} \frac{x ^{2}}{2}

Simplify

- e^{2 x} \frac{x ^{3}}{3} - e^{2 x} \frac{x ^{2}}{2} : - \frac{e ^{2 x} x ^{3}}{3} - \frac{e ^{2 x} x ^{2}}{2}

= - \frac{e ^{2 x} x ^{3}}{3} - \frac{e ^{2 x} x ^{2}}{2}

(\frac{1}{4} e^{x} - e^{- x})^{2}

6 (6 - 3)

(- 3 - i)^{7}

(x + 2 + 1)^{2}

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