What is expand (2e^x-1/8 e^{-x})^2 ?

The solution to expand (2e^x-1/8 e^{-x})^2 is 4e^{2x}-1/2+1/64 e^{-2x}

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expand (2e^x-1/8 e^{-x})^2

expand

(2 e^{x} - \frac{1}{8} e^{- x})^{2}

4 e^{2 x} - \frac{1}{2} + \frac{1}{64} e^{- 2 x}

Solution steps

(2 e^{x} - \frac{1}{8} e^{- x})^{2}

Apply Perfect Square Formula:

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

a = 2 e^{x}, b = \frac{1}{8} e^{- x}

= (2 e^{x})^{2} - 2 \cdot 2 e^{x} \frac{1}{8} e^{- x} + (\frac{1}{8} e^{- x})^{2}

Simplify

(2 e^{x})^{2} - 2 \cdot 2 e^{x} \frac{1}{8} e^{- x} + (\frac{1}{8} e^{- x})^{2} : 4 e^{2 x} - \frac{1}{2} + \frac{1}{64} e^{- 2 x}

= 4 e^{2 x} - \frac{1}{2} + \frac{1}{64} e^{- 2 x}

\frac{x ^{2} - 3 x + 16}{( x - 5 ) ( x ^{2} + 1 )}

\frac{( 8 x A + 16 x t + x A ^{2} ) ^{2}}{4 A ^{2}}

\frac{x ^{3} + y ^{3} + z ^{3}}{( x + y ) ( x + z ) ( y + z )}

(4 y + y x^{2}) d y - (2 x + x y^{2}) d x

What is expand (2e^x-1/8 e^{-x})^2 ?
The solution to expand (2e^x-1/8 e^{-x})^2 is 4e^{2x}-1/2+1/64 e^{-2x}