What is expand (e^{-4t}-e^t)^2 ?

The solution to expand (e^{-4t}-e^t)^2 is e^{-8t}-2e^{-3t}+e^{2t}

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expand (e^{-4t}-e^t)^2

expand

(e^{- 4 t} - e^{t})^{2}

e^{- 8 t} - 2 e^{- 3 t} + e^{2 t}

Solution steps

(e^{- 4 t} - e^{t})^{2}

Apply Perfect Square Formula:

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

a = e^{- 4 t}, b = e^{t}

= (e^{- 4 t})^{2} - 2 e^{- 4 t} e^{t} + (e^{t})^{2}

Simplify

(e^{- 4 t})^{2} - 2 e^{- 4 t} e^{t} + (e^{t})^{2} : e^{- 8 t} - 2 e^{- 3 t} + e^{2 t}

= e^{- 8 t} - 2 e^{- 3 t} + e^{2 t}

\frac{( ( x - 1 ) ( y + 2 ) )}{( ( y - x ) ( y - x ^{3} ) )}

3 (5 + 11)

(x^{2} + \frac{2}{x})^{10}

\frac{x ( 1 - x ) ^{3}}{3}

What is expand (e^{-4t}-e^t)^2 ?
The solution to expand (e^{-4t}-e^t)^2 is e^{-8t}-2e^{-3t}+e^{2t}