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

The solution to expand (4e^{3x}-e^{-6x})^2 is 16e^{6x}-8e^{-3x}+e^{-12x}

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expand (4e^{3x}-e^{-6x})^2

expand

(4 e^{3 x} - e^{- 6 x})^{2}

16 e^{6 x} - 8 e^{- 3 x} + e^{- 12 x}

Solution steps

(4 e^{3 x} - e^{- 6 x})^{2}

Apply Perfect Square Formula:

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

a = 4 e^{3 x}, b = e^{- 6 x}

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

Simplify

(4 e^{3 x})^{2} - 2 \cdot 4 e^{3 x} e^{- 6 x} + (e^{- 6 x})^{2} : 16 e^{6 x} - 8 e^{- 3 x} + e^{- 12 x}

= 16 e^{6 x} - 8 e^{- 3 x} + e^{- 12 x}

\frac{5 ( 351 + 6765 )}{186}

(x + 2)^{3} d x

- 5^{6}

- 5^{4}

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

What is expand (4e^{3x}-e^{-6x})^2 ?
The solution to expand (4e^{3x}-e^{-6x})^2 is 16e^{6x}-8e^{-3x}+e^{-12x}