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

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

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expand (a^{2/3}-x^{2/3})^3

expand

(a^{\frac{2}{3}} - x^{\frac{2}{3}})^{3}

a^{2} - 3 a^{\frac{4}{3}} x^{\frac{2}{3}} + 3 a^{\frac{2}{3}} x^{\frac{4}{3}} - x^{2}

Solution steps

(a^{\frac{2}{3}} - x^{\frac{2}{3}})^{3}

Apply Perfect Cube Formula:

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

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

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

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

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

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

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

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

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