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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

e^{(l n (x) - a)^{2}}

\frac{k ^{2} ( k + 1 ) ^{2}}{4} + (k + 1)

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

\frac{( ( - x + 9 ) ( x - 3 ) )}{2}

\frac{π}{32} \cdot ((0.051)^{4} - (0, 41)^{4})

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