What is expand (x^2+y^3)^3 ?

The solution to expand (x^2+y^3)^3 is x^6+3x^4y^3+3x^2y^6+y^9

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expand (x^2+y^3)^3

expand

(x^{2} + y^{3})^{3}

x^{6} + 3 x^{4} y^{3} + 3 x^{2} y^{6} + y^{9}

Solution steps

(x^{2} + y^{3})^{3}

Apply Perfect Cube Formula:

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

(x^{2} + y^{3})^{3} = (x^{2})^{3} + 3 (x^{2})^{2} y^{3} + 3 x^{2} (y^{3})^{2} + (y^{3})^{3}

= (x^{2})^{3} + 3 (x^{2})^{2} y^{3} + 3 x^{2} (y^{3})^{2} + (y^{3})^{3}

Simplify

(x^{2})^{3} + 3 (x^{2})^{2} y^{3} + 3 x^{2} (y^{3})^{2} + (y^{3})^{3} : x^{6} + 3 x^{4} y^{3} + 3 x^{2} y^{6} + y^{9}

= x^{6} + 3 x^{4} y^{3} + 3 x^{2} y^{6} + y^{9}

(- 5 x^{2} + 10 x - 1) - (6 x^{2} - x + 3)

x^{2} y^{4} (- 4 x^{4} y^{2})

(x - 1)^{2} - 16 y^{2}

4 + (- 12)

- 1 \cdot (- i)

What is expand (x^2+y^3)^3 ?
The solution to expand (x^2+y^3)^3 is x^6+3x^4y^3+3x^2y^6+y^9