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

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

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

expand

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

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

Solution steps

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

Apply Difference of Two Squares Formula:

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

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

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

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

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

\frac{3 ^{7}}{3 ^{5}}

- \frac{( x - 2 ) ( x + 2 )}{x}

\frac{g ( 5 - t )}{2}

\frac{3 x + 1}{x ( 4 - x )}

(1 - e)^{2}

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