What is expand (1/4 e^x-e^{-x})^2 ?

The solution to expand (1/4 e^x-e^{-x})^2 is 1/16 e^{2x}-1/2+e^{-2x}

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expand (1/4 e^x-e^{-x})^2

expand

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

\frac{1}{16} e^{2 x} - \frac{1}{2} + e^{- 2 x}

Solution steps

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

Apply Perfect Square Formula:

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

a = \frac{1}{4} e^{x}, b = e^{- x}

= (\frac{1}{4} e^{x})^{2} - 2 \cdot \frac{1}{4} e^{x} e^{- x} + (e^{- x})^{2}

Simplify

(\frac{1}{4} e^{x})^{2} - 2 \cdot \frac{1}{4} e^{x} e^{- x} + (e^{- x})^{2} : \frac{1}{16} e^{2 x} - \frac{1}{2} + e^{- 2 x}

= \frac{1}{16} e^{2 x} - \frac{1}{2} + e^{- 2 x}

6 (6 - 3)

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What is expand (1/4 e^x-e^{-x})^2 ?
The solution to expand (1/4 e^x-e^{-x})^2 is 1/16 e^{2x}-1/2+e^{-2x}