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

The solution to expand (3e^{3x}+4e^{-4x})^3 is 27e^{9x}+108e^{2x}+144e^{-5x}+64e^{-12x}

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expand (3e^{3x}+4e^{-4x})^3

expand

(3 e^{3 x} + 4 e^{- 4 x})^{3}

27 e^{9 x} + 108 e^{2 x} + 144 e^{- 5 x} + 64 e^{- 12 x}

Solution steps

(3 e^{3 x} + 4 e^{- 4 x})^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

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

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

Simplify

(3 e^{3 x})^{3} + 3 (3 e^{3 x})^{2} \cdot 4 e^{- 4 x} + 3 \cdot 3 e^{3 x} (4 e^{- 4 x})^{2} + (4 e^{- 4 x})^{3} : 27 e^{9 x} + 108 e^{2 x} + 144 e^{- 5 x} + 64 e^{- 12 x}

= 27 e^{9 x} + 108 e^{2 x} + 144 e^{- 5 x} + 64 e^{- 12 x}

\frac{a ( b - c )}{d}

(e^{\frac{x}{10}} - e^{- \frac{x}{10}})^{2}

2 (x (x + 2))

(e^{i z} - e^{- i z})^{3}

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

What is expand (3e^{3x}+4e^{-4x})^3 ?
The solution to expand (3e^{3x}+4e^{-4x})^3 is 27e^{9x}+108e^{2x}+144e^{-5x}+64e^{-12x}