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

The solution to expand (-3x^2+2x)^3 is -27x^6+54x^5-36x^4+8x^3

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

expand

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

- 27 x^{6} + 54 x^{5} - 36 x^{4} + 8 x^{3}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

(- 3 x^{2})^{3} + 3 (- 3 x^{2})^{2} \cdot 2 x + 3 (- 3 x^{2}) (2 x)^{2} + (2 x)^{3} : - 27 x^{6} + 54 x^{5} - 36 x^{4} + 8 x^{3}

= - 27 x^{6} + 54 x^{5} - 36 x^{4} + 8 x^{3}

- 2 \frac{1}{3}

\frac{( 2 x + 3 ) - 3}{2}

\frac{x}{9} + \frac{7 x}{6}

(2 + 2 x)^{2}

What is expand (-3x^2+2x)^3 ?
The solution to expand (-3x^2+2x)^3 is -27x^6+54x^5-36x^4+8x^3