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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand ((e^x-x)^3)/3

expand

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

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

Solution steps

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

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

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

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

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

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

Divide the numbers:

\frac{3}{3} = 1

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

3 ((3, - 2) - 2 (- 1, 1))

- 73 (- 4 e - 3)

cos (2 (t - x))

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

\frac{1}{( a + 5 ) ^{2}}

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