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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

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

- \frac{6}{( 3 - 1 ) ^{4}} + cos (3 - 1)

x^{2} (sin (x + y^{2}) + 2 y^{2} cos (x + y^{2}))

x (86 - \frac{x}{18})

(- 8 + 43) (- 4 - 810)

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