What is expand (9+e^{-6x})^2 ?

The solution to expand (9+e^{-6x})^2 is 81+18e^{-6x}+e^{-12x}

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expand (9+e^{-6x})^2

expand

(9 + e^{- 6 x})^{2}

81 + 18 e^{- 6 x} + e^{- 12 x}

Solution steps

(9 + e^{- 6 x})^{2}

Apply Perfect Square Formula:

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

a = 9, b = e^{- 6 x}

= 9^{2} + 2 \cdot 9 e^{- 6 x} + (e^{- 6 x})^{2}

Simplify

9^{2} + 2 \cdot 9 e^{- 6 x} + (e^{- 6 x})^{2} : 81 + 18 e^{- 6 x} + e^{- 12 x}

= 81 + 18 e^{- 6 x} + e^{- 12 x}

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What is expand (9+e^{-6x})^2 ?
The solution to expand (9+e^{-6x})^2 is 81+18e^{-6x}+e^{-12x}