What is expand (x^{1/3}-1)^3 ?

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

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expand (x^{1/3}-1)^3

expand

(x^{\frac{1}{3}} - 1)^{3}

x - 3 x^{\frac{2}{3}} + 3 x^{\frac{1}{3}} - 1

Solution steps

(x^{\frac{1}{3}} - 1)^{3}

Apply Perfect Cube Formula:

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

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

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

(x^{\frac{1}{3}})^{3} = x

3 (x^{\frac{1}{3}})^{2} \cdot 1 = 3 x^{\frac{2}{3}}

3 x^{\frac{1}{3}} \cdot 1^{2} = 3 x^{\frac{1}{3}}

1^{3} = 1

= x - 3 x^{\frac{2}{3}} + 3 x^{\frac{1}{3}} - 1

(\frac{5}{1 - x} - \frac{4}{1 + 2 x})^{4}

(1 + 3) x

23 (2 x + 33)

\frac{( - m ^{2} + a ^{2} ) ( a ^{2} + am + m ^{2} )}{4 + m}

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