What is expand (8-4e^{-x})^2 ?

The solution to expand (8-4e^{-x})^2 is 64-64e^{-x}+16e^{-2x}

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expand (8-4e^{-x})^2

expand

(8 - 4 e^{- x})^{2}

64 - 64 e^{- x} + 16 e^{- 2 x}

Solution steps

(8 - 4 e^{- x})^{2}

Apply Perfect Square Formula:

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

a = 8, b = 4 e^{- x}

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

Simplify

8^{2} - 2 \cdot 8 \cdot 4 e^{- x} + (4 e^{- x})^{2} : 64 - 64 e^{- x} + 16 e^{- 2 x}

= 64 - 64 e^{- x} + 16 e^{- 2 x}

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What is expand (8-4e^{-x})^2 ?
The solution to expand (8-4e^{-x})^2 is 64-64e^{-x}+16e^{-2x}