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

The solution to expand (e^{-3t}+e^{3t})^3 is e^{-9t}+3e^{-3t}+3e^{3t}+e^{9t}

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

expand

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

e^{- 9 t} + 3 e^{- 3 t} + 3 e^{3 t} + e^{9 t}

Solution steps

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

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

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

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

Simplify

(e^{- 3 t})^{3} + 3 (e^{- 3 t})^{2} e^{3 t} + 3 e^{- 3 t} (e^{3 t})^{2} + (e^{3 t})^{3} : e^{- 9 t} + 3 e^{- 3 t} + 3 e^{3 t} + e^{9 t}

= e^{- 9 t} + 3 e^{- 3 t} + 3 e^{3 t} + e^{9 t}

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

\frac{n ( n + 2 ) ( n + 3 ) ( n + 4 )}{4}

y (- e^{- y} = x^{3} + c)

\frac{5 s + 3}{( s - 1 ) ( s ^{2} + 2 s + 5 )}

e^{(50 - t)^{2}} - 2 (50 - t) + c

What is expand (e^{-3t}+e^{3t})^3 ?
The solution to expand (e^{-3t}+e^{3t})^3 is e^{-9t}+3e^{-3t}+3e^{3t}+e^{9t}