What is expand (e^x-1)^3 ?

The solution to expand (e^x-1)^3 is e^{3x}-3e^{2x}+3e^x-1

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expand (e^x-1)^3

expand

(e^{x} - 1)^{3}

e^{3 x} - 3 e^{2 x} + 3 e^{x} - 1

Solution steps

(e^{x} - 1)^{3}

Apply Perfect Cube Formula:

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

a = e^{x}, b = 1

= (e^{x})^{3} - 3 (e^{x})^{2} \cdot 1 + 3 e^{x} \cdot 1^{2} - 1^{3}

Simplify

(e^{x})^{3} - 3 (e^{x})^{2} \cdot 1 + 3 e^{x} \cdot 1^{2} - 1^{3} : e^{3 x} - 3 e^{2 x} + 3 e^{x} - 1

= e^{3 x} - 3 e^{2 x} + 3 e^{x} - 1

cos (x) (tan (x) + sec (x))

(- 1 + \frac{4 i}{n})^{3}

\frac{2 s - 4}{( s ^{2} + s ) ( s ^{2} + 1 )}

(2 sin (x) - 1) (sin (x) + 2)

sin ((2 n - 1) \frac{π}{4})

What is expand (e^x-1)^3 ?
The solution to expand (e^x-1)^3 is e^{3x}-3e^{2x}+3e^x-1