What is expand (1+3e^{-x})^2 ?

The solution to expand (1+3e^{-x})^2 is 1+6e^{-x}+9e^{-2x}

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expand (1+3e^{-x})^2

expand

(1 + 3 e^{- x})^{2}

1 + 6 e^{- x} + 9 e^{- 2 x}

Solution steps

(1 + 3 e^{- x})^{2}

Apply Perfect Square Formula:

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

a = 1, b = 3 e^{- x}

= 1^{2} + 2 \cdot 1 \cdot 3 e^{- x} + (3 e^{- x})^{2}

Simplify

1^{2} + 2 \cdot 1 \cdot 3 e^{- x} + (3 e^{- x})^{2} : 1 + 6 e^{- x} + 9 e^{- 2 x}

= 1 + 6 e^{- x} + 9 e^{- 2 x}

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\frac{\partial}{\partial r} ((x) (r + 3 s - t))

What is expand (1+3e^{-x})^2 ?
The solution to expand (1+3e^{-x})^2 is 1+6e^{-x}+9e^{-2x}