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

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

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

expand

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

4 e^{4 x} - 8 + 4 e^{- 4 x}

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

= 4 e^{4 x} - 8 + 4 e^{- 4 x}

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