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

The solution to expand (e^{-2x}+1)^2 is e^{-4x}+2e^{-2x}+1

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

expand

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

e^{- 4 x} + 2 e^{- 2 x} + 1

Solution steps

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

Apply Perfect Square Formula:

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

a = e^{- 2 x}, b = 1

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

Simplify

(e^{- 2 x})^{2} + 2 e^{- 2 x} \cdot 1 + 1^{2} : e^{- 4 x} + 2 e^{- 2 x} + 1

= e^{- 4 x} + 2 e^{- 2 x} + 1

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What is expand (e^{-2x}+1)^2 ?
The solution to expand (e^{-2x}+1)^2 is e^{-4x}+2e^{-2x}+1