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}

(q + 2) \cdot (q - 2)

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

(x sin (x)) (cos (x) - x sin (x))

(2 x - 3) (x)

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

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