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

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

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expand (e^x-2)^3

expand

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

e^{3 x} - 6 e^{2 x} + 12 e^{x} - 8

Solution steps

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

Apply Perfect Cube Formula:

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

a = e^{x}, b = 2

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

Simplify

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

= e^{3 x} - 6 e^{2 x} + 12 e^{x} - 8

\frac{d}{d y} ((z) (z^{3} - x y + y z + y^{3} - 2))

\frac{1 + sin ( x ) ( 1 - sin ( x ) )}{cos ( x )}

(x^{2} + 2 x y - y^{2}) d x + (y^{2} + 2 x y - x^{2}) d y

24 e^{(- 20 t)} + 20 (\frac{6}{5} - \frac{6}{5} e^{(- 20 t)})

\frac{d}{d t} ((x) (2 x + \frac{2 y}{3}))

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