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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

(x + \frac{4}{5}) (x - \frac{3}{5})

x x (3 ln (x) - 2)

(1 + 5)^{5}

\frac{1}{( s + 3 ) ^{2}}

(x^{2} + \frac{1}{x})^{12}

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