What is expand-1/12 (2-3e^x)^4 ?

The solution to expand-1/12 (2-3e^x)^4 is -4/3+8e^x-18e^{2x}+18e^{3x}-27/4 e^{4x}

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expand-1/12 (2-3e^x)^4

expand

- \frac{1}{12} (2 - 3 e^{x})^{4}

- \frac{4}{3} + 8 e^{x} - 18 e^{2 x} + 18 e^{3 x} - \frac{27}{4} e^{4 x}

Solution steps

- \frac{1}{12} (2 - 3 e^{x})^{4}

(2 - 3 e^{x})^{4} = 16 - 96 e^{x} + 216 e^{2 x} - 216 e^{3 x} + 81 e^{4 x}

= - \frac{1}{12} (- 96 e^{x} + 216 e^{2 x} + 81 e^{4 x} - 216 e^{3 x} + 16)

Distribute parentheses

= (- \frac{1}{12}) \cdot 16 + (- \frac{1}{12}) (- 96 e^{x}) + (- \frac{1}{12}) \cdot 216 e^{2 x} + (- \frac{1}{12}) (- 216 e^{3 x}) + (- \frac{1}{12}) \cdot 81 e^{4 x}

Apply minus-plus rules

+ (- a) = - a, (- a) (- b) = ab

= - 16 \cdot \frac{1}{12} + 96 \cdot \frac{1}{12} e^{x} - 216 \cdot \frac{1}{12} e^{2 x} + 216 \cdot \frac{1}{12} e^{3 x} - 81 \cdot \frac{1}{12} e^{4 x}

Simplify

- 16 \cdot \frac{1}{12} + 96 \cdot \frac{1}{12} e^{x} - 216 \cdot \frac{1}{12} e^{2 x} + 216 \cdot \frac{1}{12} e^{3 x} - 81 \cdot \frac{1}{12} e^{4 x} : - \frac{4}{3} + 8 e^{x} - 18 e^{2 x} + 18 e^{3 x} - \frac{27}{4} e^{4 x}

= - \frac{4}{3} + 8 e^{x} - 18 e^{2 x} + 18 e^{3 x} - \frac{27}{4} e^{4 x}

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

(\frac{5 r ^{7}}{6} + \frac{p ^{4} q}{7}) (\frac{p ^{4} q}{7} - \frac{5 r ^{7}}{6})

(1 - e^{- \frac{t}{RC}})^{2}

\frac{d}{d x} ((20) (x + \frac{3000}{x})) + \frac{12000}{x}

(2 \cdot x) \cdot (x^{2} + 1)

What is expand-1/12 (2-3e^x)^4 ?
The solution to expand-1/12 (2-3e^x)^4 is -4/3+8e^x-18e^{2x}+18e^{3x}-27/4 e^{4x}