What is expand ((e^{5x}-e^{-5x})^2)/4 ?

The solution to expand ((e^{5x}-e^{-5x})^2)/4 is (e^{10x})/4-1/2+(e^{-10x})/4

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expand ((e^{5x}-e^{-5x})^2)/4

expand

\frac{( e ^{5 x} - e ^{- 5 x} ) ^{2}}{4}

\frac{e ^{10 x}}{4} - \frac{1}{2} + \frac{e ^{- 10 x}}{4}

Solution steps

\frac{( e ^{5 x} - e ^{- 5 x} ) ^{2}}{4}

(e^{5 x} - e^{- 5 x})^{2} = e^{10 x} - 2 + e^{- 10 x}

= \frac{e ^{10 x} - 2 + e ^{- 10 x}}{4}

Apply the fraction rule:

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

\frac{e ^{10 x} - 2 + e ^{- 10 x}}{4} = \frac{e ^{10 x}}{4} - \frac{2}{4} + \frac{e ^{- 10 x}}{4}

= \frac{e ^{10 x}}{4} - \frac{2}{4} + \frac{e ^{- 10 x}}{4}

Cancel

\frac{2}{4} : \frac{1}{2}

= \frac{e ^{10 x}}{4} - \frac{1}{2} + \frac{e ^{- 10 x}}{4}

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What is expand ((e^{5x}-e^{-5x})^2)/4 ?
The solution to expand ((e^{5x}-e^{-5x})^2)/4 is (e^{10x})/4-1/2+(e^{-10x})/4