What is expand (2+6e^{-2x})^2 ?

The solution to expand (2+6e^{-2x})^2 is 4+24e^{-2x}+36e^{-4x}

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expand (2+6e^{-2x})^2

expand

(2 + 6 e^{- 2 x})^{2}

4 + 24 e^{- 2 x} + 36 e^{- 4 x}

Solution steps

(2 + 6 e^{- 2 x})^{2}

Apply Perfect Square Formula:

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

a = 2, b = 6 e^{- 2 x}

= 2^{2} + 2 \cdot 2 \cdot 6 e^{- 2 x} + (6 e^{- 2 x})^{2}

Simplify

2^{2} + 2 \cdot 2 \cdot 6 e^{- 2 x} + (6 e^{- 2 x})^{2} : 4 + 24 e^{- 2 x} + 36 e^{- 4 x}

= 4 + 24 e^{- 2 x} + 36 e^{- 4 x}

\frac{( 1 + 6 x ) ^{5}}{5}

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

2 (ln (2 x) + β)

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

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

What is expand (2+6e^{-2x})^2 ?
The solution to expand (2+6e^{-2x})^2 is 4+24e^{-2x}+36e^{-4x}