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

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

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

expand

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

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

Solution steps

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

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

\frac{5 x}{( x + 1 ) ^{2}}

\frac{( x + y ) ^{2}}{2}

\frac{5 ( f - 32 )}{9}

(- 3, 2) y (7, - 3)

(x + 1) e^{2 x}

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