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

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

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

expand

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

\frac{27 - 54 x ^{3} + 36 x ^{6} - 8 x ^{9}}{x ^{3}}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

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

= \frac{27 - 54 x ^{3} + 36 x ^{6} - 8 x ^{9}}{x ^{3}}

lo g_{10} (x^{5} y z^{3})

(1 + sin (a)) (1 - sin (a))

(a x + b y) (c x + d y)

\frac{2 ( x ^{2} - 9 )}{x ^{2} - 4}

\frac{x ^{2} + 5}{( x - 1 ) ( x ^{2} + 4 ) ^{2}}

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