What is expand (1/2-x/3)x^2e^{2x} ?

The solution to expand (1/2-x/3)x^2e^{2x} is (e^{2x}x^2)/2-(e^{2x}x^3)/3

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expand (1/2-x/3)x^2e^{2x}

expand

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

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

Solution steps

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

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

Apply the distributive law:

a (b - c) = ab - a c

a = x^{2} e^{2 x}, b = \frac{1}{2}, c = \frac{x}{3}

= x^{2} e^{2 x} \frac{1}{2} - x^{2} e^{2 x} \frac{x}{3}

= \frac{1}{2} e^{2 x} x^{2} - e^{2 x} x^{2} \frac{x}{3}

Simplify

\frac{1}{2} e^{2 x} x^{2} - e^{2 x} x^{2} \frac{x}{3} : \frac{e ^{2 x} x ^{2}}{2} - \frac{e ^{2 x} x ^{3}}{3}

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

6.9 (e^{- 0.24 t} - 0.24 e^{- 0.24 t} t)

2 (2 csc (2 x) + x (- csc^{2} (x) + sec^{2} (x)))

\frac{d ^{3} y}{d ^{3} x} (x^{2} + x y + y^{3} = 1)

sin ((n - 1) π)

2 cos^{2} (3 t) + 2 (e^{t} + 1)^{2}

What is expand (1/2-x/3)x^2e^{2x} ?
The solution to expand (1/2-x/3)x^2e^{2x} is (e^{2x}x^2)/2-(e^{2x}x^3)/3