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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (e^{-2t}-e^{-t})^2

expand

(e^{- 2 t} - e^{- t})^{2}

e^{- 4 t} - 2 e^{- 3 t} + e^{- 2 t}

Solution steps

(e^{- 2 t} - e^{- t})^{2}

Apply Perfect Square Formula:

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

a = e^{- 2 t}, b = e^{- t}

= (e^{- 2 t})^{2} - 2 e^{- 2 t} e^{- t} + (e^{- t})^{2}

Simplify

(e^{- 2 t})^{2} - 2 e^{- 2 t} e^{- t} + (e^{- t})^{2} : e^{- 4 t} - 2 e^{- 3 t} + e^{- 2 t}

= e^{- 4 t} - 2 e^{- 3 t} + e^{- 2 t}

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

(- 3, 3) y (- 1, - 5)

\frac{( 2 x ^{3} - 8 x ^{2} + 9 x - 2 )}{( x - 2 )}

x \cdot (e^{\frac{1}{x}} - 1)

- \frac{2 ( 6 x ^{2} + x - 332 )}{( x + 8 ) ( x + 7 ) ( x - 3 )}

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