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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

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