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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

(4 + 3 i)^{6}

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