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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

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

\frac{x ^{3}}{( x ^{2} + 1 ) ( x ^{4} - x ^{2} + 1 )}

\frac{1}{a s ^{2}} - \frac{e ^{- a s}}{s ( 1 - e ^{- a s} )}

\frac{( a + b - 2 ab ) ( a + b )}{a - b}

\frac{x ( x + 1 )}{x + 4}

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