What is expand (2e^{3x}-e^{-3x})^2 ?

The solution to expand (2e^{3x}-e^{-3x})^2 is 4e^{6x}-4+e^{-6x}

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expand (2e^{3x}-e^{-3x})^2

expand

(2 e^{3 x} - e^{- 3 x})^{2}

4 e^{6 x} - 4 + e^{- 6 x}

Solution steps

(2 e^{3 x} - e^{- 3 x})^{2}

Apply Perfect Square Formula:

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

a = 2 e^{3 x}, b = e^{- 3 x}

= (2 e^{3 x})^{2} - 2 \cdot 2 e^{3 x} e^{- 3 x} + (e^{- 3 x})^{2}

Simplify

(2 e^{3 x})^{2} - 2 \cdot 2 e^{3 x} e^{- 3 x} + (e^{- 3 x})^{2} : 4 e^{6 x} - 4 + e^{- 6 x}

= 4 e^{6 x} - 4 + e^{- 6 x}

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What is expand (2e^{3x}-e^{-3x})^2 ?
The solution to expand (2e^{3x}-e^{-3x})^2 is 4e^{6x}-4+e^{-6x}