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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

\frac{3}{( 1 - x ) ^{2}}

2 (62 + 19) (62 - 19)

x (x - 1)

3 x^{2} + 6 x y + (3 x^{2} + 2 y) \frac{d y}{d x}

3^{2}

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