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

The solution to expand (4e^{-2x}-e^{-4x})^2 is 16e^{-4x}-8e^{-6x}+e^{-8x}

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

expand

(4 e^{- 2 x} - e^{- 4 x})^{2}

16 e^{- 4 x} - 8 e^{- 6 x} + e^{- 8 x}

Solution steps

(4 e^{- 2 x} - e^{- 4 x})^{2}

Apply Perfect Square Formula:

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

a = 4 e^{- 2 x}, b = e^{- 4 x}

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

Simplify

(4 e^{- 2 x})^{2} - 2 \cdot 4 e^{- 2 x} e^{- 4 x} + (e^{- 4 x})^{2} : 16 e^{- 4 x} - 8 e^{- 6 x} + e^{- 8 x}

= 16 e^{- 4 x} - 8 e^{- 6 x} + e^{- 8 x}

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What is expand (4e^{-2x}-e^{-4x})^2 ?
The solution to expand (4e^{-2x}-e^{-4x})^2 is 16e^{-4x}-8e^{-6x}+e^{-8x}