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

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

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

expand

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

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

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

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

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

2 x^{3} - 5 x^{2} - 4 x + 10

\frac{- 4 x ^{8} y ^{4}}{12 x ^{2} y}

\frac{3}{4} + \frac{2}{3} + \frac{1}{2}

(x + 6) (2 x + 4)

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