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

The solution to expand (3+e^{-2t})^2 is 9+6e^{-2t}+e^{-4t}

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

expand

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

9 + 6 e^{- 2 t} + e^{- 4 t}

Solution steps

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

Apply Perfect Square Formula:

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

a = 3, b = e^{- 2 t}

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

Simplify

3^{2} + 2 \cdot 3 e^{- 2 t} + (e^{- 2 t})^{2} : 9 + 6 e^{- 2 t} + e^{- 4 t}

= 9 + 6 e^{- 2 t} + e^{- 4 t}

\frac{8 x - 42}{( x ^{2} + 1 ) ^{2}}

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r ((x, y) + (a, b))

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4 (x - 2) (x + \frac{1}{3})

What is expand (3+e^{-2t})^2 ?
The solution to expand (3+e^{-2t})^2 is 9+6e^{-2t}+e^{-4t}