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

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

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expand (xe^{-x}+x)(xe^{-x}-x)

expand

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

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

Solution steps

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

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

Apply Difference of Two Squares Formula:

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

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

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

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

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

- e^{- r t} (x + u)^{0.5} + p (x - u)

\frac{2 ( 5 m + 1 )}{m - 6}

\frac{( ( R - S + S cos ( θ ) ) )}{R}

(x + 1) y d x - (y + 1) x d y

sech (5.54)

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