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

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

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expand (x^{1/3}+y^{1/3})^3

expand

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

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

Solution steps

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

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

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

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

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

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

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

\frac{cos ( \frac{π x}{2} ) ( 1 + x )}{1 - x}

\frac{n ^{2} ( n + 1 ) ^{2} ( 2 n ^{2} + 2 n - 1 )}{12}

\frac{x + 2}{( x + 4 ) ( x + 1 )}

(x - a - bi) (x - c - d i) (x - e - f i) (x - g - hi)

(3, 5) y (1, - 1)

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