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

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

Simplify

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

8 r + 12 p - 7 - 3 p

π (2 x + 1)^{2} (2 x - 1)

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

(5 x^{\frac{1}{2}} + 3) (5 x^{\frac{1}{2}} - 3)

- \frac{x + 1}{( x - 1 ) ^{3}}

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