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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

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

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

(1 + y^{2}) d x + (x^{2} y + y) d y

\frac{20}{( S + 1 ) ( S ^{2} + 4 S + 13 )}

\frac{x ^{3} + 1}{x ( x - 1 ) ^{3}}

\frac{1}{( x + c ) ( x )}

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

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