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

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

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

expand

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

e^{4 x} + 2 + e^{- 4 x}

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

\frac{( s + 1 ) ( s + 2 )}{s ^{4}}

(x + h)^{2} - 3

((m - 1) + 1)^{n}

\frac{sin ^{2} ( x ^{2} - 4 )}{( x + 2 ) tan ( x + 2 )}

\frac{( r - 1 ) ( r + 49 )}{r ^{2} - 49}

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