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

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

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

expand

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

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

Solution steps

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

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

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

Apply the fraction rule:

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

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

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

Apply rule

\frac{a}{a} = 1

\frac{2}{2} = 1

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

(4^{x} + e^{x})^{2}

26 - 4 x (x = - 3)

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

a c - b d + i (a d + b c)

\frac{2 - ( 1 + k ) i}{1 - ki}

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