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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

(10 x - 1) (\frac{1000 x ^{3} - 10 x + 2}{10 x - 1} + 1)

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

(\frac{x}{9} + 1)^{2}

(a e^{2}) (a^{2} + 3 a - 4)

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

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