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

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

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expand (L^t-L^{-t})^3

expand

(L^{t} - L^{- t})^{3}

L^{3 t} - 3 L^{t} + 3 L^{- t} - L^{- 3 t}

Solution steps

(L^{t} - L^{- t})^{3}

Apply Perfect Cube Formula:

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

a = L^{t}, b = L^{- t}

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

Simplify

(L^{t})^{3} - 3 (L^{t})^{2} L^{- t} + 3 L^{t} (L^{- t})^{2} - (L^{- t})^{3} : L^{3 t} - 3 L^{t} + 3 L^{- t} - L^{- 3 t}

= L^{3 t} - 3 L^{t} + 3 L^{- t} - L^{- 3 t}

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F oco (3, - 2)

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