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

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

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

expand

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

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

Solution steps

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

Apply exponent rule:

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

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

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

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

2^{2} = 4

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

Apply the fraction rule:

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

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

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

Cancel

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

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

e^{x (x - 3)}

\frac{6 x}{( 5 + 3 x ^{2} ) ^{4}}

\frac{1}{( x + 2 ) ( x - 3 )}

\frac{( x - 6 ) ^{2}}{x}

\frac{( x ^{2} - 13 x + 40 )}{( x + 1 ) ( x ^{2} - 4 x + 13 )}

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