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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

\frac{d}{d h} ((3 h^{2} + 4) 23) - 8

\frac{( 2 x ^{2} + 2 x + 1 ) ( 2 x ^{2} - 2 x + 1 )}{4 x ^{2}}

\frac{2 ( s - 1 )}{s ^{4} + s ^{2} + 1}

\frac{( x + h ) ^{3} - 3 a x ^{2} + 2 b x + c}{h}

\frac{3 x ^{2} + 5}{2 ( x - 1 ) ^{2}}

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