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

The solution to expand (e^{2x}-e^{-3x})^3 is e^{6x}-3e^x+3e^{-4x}-e^{-9x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

expand

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

e^{6 x} - 3 e^{x} + 3 e^{- 4 x} - e^{- 9 x}

Solution steps

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

Apply Perfect Cube Formula:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

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

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

Simplify

(e^{2 x})^{3} - 3 (e^{2 x})^{2} e^{- 3 x} + 3 e^{2 x} (e^{- 3 x})^{2} - (e^{- 3 x})^{3} : e^{6 x} - 3 e^{x} + 3 e^{- 4 x} - e^{- 9 x}

= e^{6 x} - 3 e^{x} + 3 e^{- 4 x} - e^{- 9 x}

(9 \cdot e^{- 9 \cdot x} + 2)^{3}

π r^{2} (84 - 2 π r)

(1 + 3 e^{- x})^{2}

x^{5} x^{2}

\frac{d}{d t} ((4) (7 + e^{- t^{2}}))

What is expand (e^{2x}-e^{-3x})^3 ?
The solution to expand (e^{2x}-e^{-3x})^3 is e^{6x}-3e^x+3e^{-4x}-e^{-9x}