What is expand ((e^x-e^{-x})/2)^3 ?

The solution to expand ((e^x-e^{-x})/2)^3 is (e^{3x})/8-(3e^x)/8+(3e^{-x})/8-(e^{-3x})/8

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expand ((e^x-e^{-x})/2)^3

expand

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

\frac{e ^{3 x}}{8} - \frac{3 e ^{x}}{8} + \frac{3 e ^{- x}}{8} - \frac{e ^{- 3 x}}{8}

Solution steps

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

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

= \frac{e ^{3 x} - 3 e ^{x} + 3 e ^{- x} - e ^{- 3 x}}{2 ^{3}}

2^{3} = 8

= \frac{e ^{3 x} - 3 e ^{x} + 3 e ^{- x} - e ^{- 3 x}}{8}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{e ^{3 x} - 3 e ^{x} + 3 e ^{- x} - e ^{- 3 x}}{8} = \frac{e ^{3 x}}{8} - \frac{3 e ^{x}}{8} + \frac{3 e ^{- x}}{8} - \frac{e ^{- 3 x}}{8}

= \frac{e ^{3 x}}{8} - \frac{3 e ^{x}}{8} + \frac{3 e ^{- x}}{8} - \frac{e ^{- 3 x}}{8}

\frac{x ^{2} ( x - 2 )}{x ^{2} - 9}

3.5 (\frac{18.6 - 4.8 x}{3. 5 ^{2}})^{2}

1 (\frac{3}{2 x})^{0} (\frac{1}{y})^{6}

(2 x + 1) (x + 9)

\frac{6}{( s - 2 ) \cdot ( s ^{2} - 4 s + 5 ) ^{2}}

What is expand ((e^x-e^{-x})/2)^3 ?
The solution to expand ((e^x-e^{-x})/2)^3 is (e^{3x})/8-(3e^x)/8+(3e^{-x})/8-(e^{-3x})/8