What is expand {(5+3e^{-2t})^2}(s) ?

The solution to expand {(5+3e^{-2t})^2}(s) is 25s+30e^{-2t}s+9e^{-4t}s

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expand {(5+3e^{-2t})^2}(s)

expand

{(5 + 3 e^{- 2 t})^{2}} (s)

25 s + 30 e^{- 2 t} s + 9 e^{- 4 t} s

Solution steps

((5 + 3 e^{- 2 t})^{2}) (s)

Remove parentheses:

(a) = a

= (5 + 3 e^{- 2 t})^{2} s

(5 + 3 e^{- 2 t})^{2} = 25 + 30 e^{- 2 t} + 9 e^{- 4 t}

= s (30 e^{- 2 t} + 9 e^{- 4 t} + 25)

= s (25 + 30 e^{- 2 t} + 9 e^{- 4 t})

Distribute parentheses

= s \cdot 25 + s \cdot 30 e^{- 2 t} + s \cdot 9 e^{- 4 t}

= 25 s + 30 e^{- 2 t} s + 9 e^{- 4 t} s

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\frac{x - 1}{( x - 5 ) ^{2}}

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

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What is expand {(5+3e^{-2t})^2}(s) ?
The solution to expand {(5+3e^{-2t})^2}(s) is 25s+30e^{-2t}s+9e^{-4t}s