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

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

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

expand

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

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

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

(1 - sin (2 x))^{2}

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

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

\frac{1}{2} + \frac{1}{4} (1.2 - 1)

(- 2 - 3 i)^{7}

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