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

The solution to expand (e^{-x}-2)^2 is e^{-2x}-4e^{-x}+4

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

expand

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

e^{- 2 x} - 4 e^{- x} + 4

Solution steps

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

Apply Perfect Square Formula:

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

a = e^{- x}, b = 2

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

Simplify

(e^{- x})^{2} - 2 e^{- x} \cdot 2 + 2^{2} : e^{- 2 x} - 4 e^{- x} + 4

= e^{- 2 x} - 4 e^{- x} + 4

2 x l e f t (3 x^{2} - 5 x + 1)

4^{2}

\frac{x - 29}{( x - 2 ) ^{2}}

(x + 1) x - 1

(9 x^{\frac{3}{2}} - 3 x^{\frac{5}{2}})^{2}

What is expand (e^{-x}-2)^2 ?
The solution to expand (e^{-x}-2)^2 is e^{-2x}-4e^{-x}+4