What is expand (e^{3t}+e^{-3t})^2 ?

The solution to expand (e^{3t}+e^{-3t})^2 is e^{6t}+2+e^{-6t}

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expand (e^{3t}+e^{-3t})^2

expand

(e^{3 t} + e^{- 3 t})^{2}

e^{6 t} + 2 + e^{- 6 t}

Solution steps

(e^{3 t} + e^{- 3 t})^{2}

Apply Perfect Square Formula:

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

a = e^{3 t}, b = e^{- 3 t}

= (e^{3 t})^{2} + 2 e^{3 t} e^{- 3 t} + (e^{- 3 t})^{2}

Simplify

(e^{3 t})^{2} + 2 e^{3 t} e^{- 3 t} + (e^{- 3 t})^{2} : e^{6 t} + 2 + e^{- 6 t}

= e^{6 t} + 2 + e^{- 6 t}

(x + y i)^{5}

(2 e^{- 0.01 t} - e^{- 0.02 t})^{3}

tan (x) (cot (x) + 1)

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

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

What is expand (e^{3t}+e^{-3t})^2 ?
The solution to expand (e^{3t}+e^{-3t})^2 is e^{6t}+2+e^{-6t}