What is expand e^x(e^x-1)^2 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand e^x(e^x-1)^2

expand

e^{x} (e^{x} - 1)^{2}

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

Solution steps

e^{x} (e^{x} - 1)^{2}

(e^{x} - 1)^{2} = e^{2 x} - 2 e^{x} + 1

= e^{x} (- 2 e^{x} + e^{2 x} + 1)

Distribute parentheses

= e^{x} e^{2 x} + e^{x} (- 2 e^{x}) + e^{x} \cdot 1

Apply minus-plus rules

+ (- a) = - a

= e^{x} e^{2 x} - 2 e^{x} e^{x} + 1 \cdot e^{x}

Simplify

e^{x} e^{2 x} - 2 e^{x} e^{x} + 1 \cdot e^{x} : e^{3 x} - 2 e^{2 x} + e^{x}

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

\frac{19 ( e ^{2} + 3 )}{3}

\frac{e ^{- s}}{( s - 1 ) ( s - 2 )}

\frac{1}{s ^{2} ( s ^{2} + w ^{2} )}

\frac{( e ^{- π s} )}{s ( s ^{2} + 4 )}

(2 x - 3) e^{3}

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