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

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

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

expand

(e^{2 jπ} + e^{- 2 jπ})^{3}

e^{6 πj} + 3 e^{2 πj} + 3 e^{- 2 πj} + e^{- 6 πj}

Solution steps

(e^{2 jπ} + e^{- 2 jπ})^{3}

= (e^{2 πj} + e^{- 2 πj})^{3}

Apply Perfect Cube Formula:

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

a = e^{2 jπ}, b = e^{- 2 jπ}

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

Simplify

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

= e^{6 πj} + 3 e^{2 πj} + 3 e^{- 2 πj} + e^{- 6 πj}

(e^{16 i x} - 1) (e^{- 8 i x} + 3 e^{8 i x} + e^{16 i x} + 3)

- \frac{( 6 x - 5 ) ( x + 5 )}{( x - 6 ) ( x + 6 ) ( x - 5 )}

2 (5 - 3)

\frac{3 b ( a ^{2} + 5 )}{c}

2 (33 - 67 + 21 - 14)

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