What is expand (2e^{3x}+e^{-3x})^2 ?

The solution to expand (2e^{3x}+e^{-3x})^2 is 4e^{6x}+4+e^{-6x}

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expand (2e^{3x}+e^{-3x})^2

expand

(2 e^{3 x} + e^{- 3 x})^{2}

4 e^{6 x} + 4 + e^{- 6 x}

Solution steps

(2 e^{3 x} + e^{- 3 x})^{2}

Apply Perfect Square Formula:

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

a = 2 e^{3 x}, b = e^{- 3 x}

= (2 e^{3 x})^{2} + 2 \cdot 2 e^{3 x} e^{- 3 x} + (e^{- 3 x})^{2}

Simplify

(2 e^{3 x})^{2} + 2 \cdot 2 e^{3 x} e^{- 3 x} + (e^{- 3 x})^{2} : 4 e^{6 x} + 4 + e^{- 6 x}

= 4 e^{6 x} + 4 + e^{- 6 x}

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

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

\frac{3 x + 5}{( x - 1 ) ( x ^{4} + 7 )}

(x + b x)^{2} + 25

What is expand (2e^{3x}+e^{-3x})^2 ?
The solution to expand (2e^{3x}+e^{-3x})^2 is 4e^{6x}+4+e^{-6x}