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

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

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

expand

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

e^{x} + 2 + e^{- x}

Solution steps

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

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

a = e^{\frac{x}{2}}, b = e^{- \frac{x}{2}}

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

Simplify

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

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

2 (7 + 4)

(1 + tan (x)) (1 - tan (x)) sec^{2} (x)

(e^{17 x} + e^{- 17 x})^{2}

2 (7 + 8)

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