What is expand (e^{8x}+e^{-8x})^2 ?

The solution to expand (e^{8x}+e^{-8x})^2 is e^{16x}+2+e^{-16x}

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expand (e^{8x}+e^{-8x})^2

expand

(e^{8 x} + e^{- 8 x})^{2}

e^{16 x} + 2 + e^{- 16 x}

Solution steps

(e^{8 x} + e^{- 8 x})^{2}

Apply Perfect Square Formula:

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

a = e^{8 x}, b = e^{- 8 x}

= (e^{8 x})^{2} + 2 e^{8 x} e^{- 8 x} + (e^{- 8 x})^{2}

Simplify

(e^{8 x})^{2} + 2 e^{8 x} e^{- 8 x} + (e^{- 8 x})^{2} : e^{16 x} + 2 + e^{- 16 x}

= e^{16 x} + 2 + e^{- 16 x}

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

(3 arctan (x) - π) (x^{2} - 3)

\frac{( n + 1 ) ( n + 2 ) ( n + 3 ) ( n + 4 )}{4}

\frac{125 ( 2 n + 1 ) ( n + 1 )}{6}

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

What is expand (e^{8x}+e^{-8x})^2 ?
The solution to expand (e^{8x}+e^{-8x})^2 is e^{16x}+2+e^{-16x}