What is expand (e^{-2t}-1)^2 ?

The solution to expand (e^{-2t}-1)^2 is e^{-4t}-2e^{-2t}+1

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expand (e^{-2t}-1)^2

expand

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

e^{- 4 t} - 2 e^{- 2 t} + 1

Solution steps

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

Apply Perfect Square Formula:

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

a = e^{- 2 t}, b = 1

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

Simplify

(e^{- 2 t})^{2} - 2 e^{- 2 t} \cdot 1 + 1^{2} : e^{- 4 t} - 2 e^{- 2 t} + 1

= e^{- 4 t} - 2 e^{- 2 t} + 1

(1 + 4 i)^{4}

\frac{1}{( x + i y ) ^{2}}

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

tan^{2} (θ) (cot^{2} (θ) - cos^{2} (θ))

\frac{1}{( x - 1 ) ( x ^{2} + 1 )}

What is expand (e^{-2t}-1)^2 ?
The solution to expand (e^{-2t}-1)^2 is e^{-4t}-2e^{-2t}+1