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

The solution to expand (2x^3-3y^2)^3 is 8x^9-36x^6y^2+54x^3y^4-27y^6

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

expand

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

8 x^{9} - 36 x^{6} y^{2} + 54 x^{3} y^{4} - 27 y^{6}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

(2 x^{3})^{3} - 3 (2 x^{3})^{2} \cdot 3 y^{2} + 3 \cdot 2 x^{3} (3 y^{2})^{2} - (3 y^{2})^{3} : 8 x^{9} - 36 x^{6} y^{2} + 54 x^{3} y^{4} - 27 y^{6}

= 8 x^{9} - 36 x^{6} y^{2} + 54 x^{3} y^{4} - 27 y^{6}

300 - 27

9 x^{2} + 5 x - 4

(x^{3} - 9 x) + (45 - 5 x^{2})

(4 a)^{3}

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

What is expand (2x^3-3y^2)^3 ?
The solution to expand (2x^3-3y^2)^3 is 8x^9-36x^6y^2+54x^3y^4-27y^6