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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

\frac{2 ( 5 n + 2 )}{n}

\frac{1}{s ( s + 2 ) ( s + 10 ) ( s + 15 )}

π (e ln^{2} (2 e) - 2 e + ln (2 e) + 1)

\frac{x ^{2} - ( k + 2 ) x + 6}{x - k}

(- 2 + 62) (3 + 1)^{5}

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