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

The solution to expand (6+e^{-6t})^2 is 36+12e^{-6t}+e^{-12t}

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

expand

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

36 + 12 e^{- 6 t} + e^{- 12 t}

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

6^{2} + 2 \cdot 6 e^{- 6 t} + (e^{- 6 t})^{2} : 36 + 12 e^{- 6 t} + e^{- 12 t}

= 36 + 12 e^{- 6 t} + e^{- 12 t}

\frac{( s - 1 )}{s ^{2} ( s + 1 ) ( s - 2 )}

\frac{( 9 + y ^{4} ) sin ( x )}{y}

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(6 + e^{- 6 t})^{4}

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What is expand (6+e^{-6t})^2 ?
The solution to expand (6+e^{-6t})^2 is 36+12e^{-6t}+e^{-12t}