What is expand (3+e^{-6t})^2 ?

The solution to expand (3+e^{-6t})^2 is 9+6e^{-6t}+e^{-12t}

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expand (3+e^{-6t})^2

expand

(3 + e^{- 6 t})^{2}

9 + 6 e^{- 6 t} + e^{- 12 t}

Solution steps

(3 + e^{- 6 t})^{2}

Apply Perfect Square Formula:

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

a = 3, b = e^{- 6 t}

= 3^{2} + 2 \cdot 3 e^{- 6 t} + (e^{- 6 t})^{2}

Simplify

3^{2} + 2 \cdot 3 e^{- 6 t} + (e^{- 6 t})^{2} : 9 + 6 e^{- 6 t} + e^{- 12 t}

= 9 + 6 e^{- 6 t} + e^{- 12 t}

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What is expand (3+e^{-6t})^2 ?
The solution to expand (3+e^{-6t})^2 is 9+6e^{-6t}+e^{-12t}