What is expand (x^{2/3}-y^{1/3})^3 ?

The solution to expand (x^{2/3}-y^{1/3})^3 is x^2-3x^{4/3}y^{1/3}+3x^{2/3}y^{2/3}-y

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expand (x^{2/3}-y^{1/3})^3

expand

(x^{\frac{2}{3}} - y^{\frac{1}{3}})^{3}

x^{2} - 3 x^{\frac{4}{3}} y^{\frac{1}{3}} + 3 x^{\frac{2}{3}} y^{\frac{2}{3}} - y

Solution steps

(x^{\frac{2}{3}} - y^{\frac{1}{3}})^{3}

Apply Perfect Cube Formula:

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

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

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

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

(x^{\frac{2}{3}})^{2} = x^{\frac{4}{3}}

(y^{\frac{1}{3}})^{2} = y^{\frac{2}{3}}

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

= x^{2} - 3 x^{\frac{4}{3}} y^{\frac{1}{3}} + 3 x^{\frac{2}{3}} y^{\frac{2}{3}} - y

(x + 37) (x - 7)

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

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

(x^{2} + 6 y^{2}) d x - 4 x y d y

(x^{2} - x + \frac{1}{6})^{2}

What is expand (x^{2/3}-y^{1/3})^3 ?
The solution to expand (x^{2/3}-y^{1/3})^3 is x^2-3x^{4/3}y^{1/3}+3x^{2/3}y^{2/3}-y