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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

f (x^{5} - 3 x^{3} + 9) d x

(e^{- 2 x} + 4) d y

(e^{2 y} + e^{- 2 y})^{2}

\frac{1}{s ^{3} ( s ^{3} - 2 s )}

2^{3} \cdot 2^{4}

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