What is expand (5+e^{-2t})^2 ?

The solution to expand (5+e^{-2t})^2 is 25+10e^{-2t}+e^{-4t}

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expand (5+e^{-2t})^2

expand

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

25 + 10 e^{- 2 t} + e^{- 4 t}

Solution steps

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

Apply Perfect Square Formula:

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

a = 5, b = e^{- 2 t}

= 5^{2} + 2 \cdot 5 e^{- 2 t} + (e^{- 2 t})^{2}

Simplify

5^{2} + 2 \cdot 5 e^{- 2 t} + (e^{- 2 t})^{2} : 25 + 10 e^{- 2 t} + e^{- 4 t}

= 25 + 10 e^{- 2 t} + e^{- 4 t}

\frac{1}{4} (1 + s) (1 + t) + \frac{1}{4} (1 - s) (1 + t)

\frac{( 5 y - 3 ) ^{2}}{25}

2 (\frac{π}{4} + 1)

240 (6 - \frac{8}{x + 2})

(3 x + \frac{4}{5}) (3 x - \frac{4}{5})

What is expand (5+e^{-2t})^2 ?
The solution to expand (5+e^{-2t})^2 is 25+10e^{-2t}+e^{-4t}