What is expand (x^2(3y-2x))/6 ?

The solution to expand (x^2(3y-2x))/6 is (x^2y)/2-(x^3)/3

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expand (x^2(3y-2x))/6

expand

\frac{x ^{2} ( 3 y - 2 x )}{6}

\frac{x ^{2} y}{2} - \frac{x ^{3}}{3}

Solution steps

\frac{x ^{2} ( 3 y - 2 x )}{6}

Expand

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

= \frac{3 x ^{2} y - 2 x ^{3}}{6}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{3 x ^{2} y - 2 x ^{3}}{6} = \frac{3 x ^{2} y}{6} - \frac{2 x ^{3}}{6}

= \frac{3 x ^{2} y}{6} - \frac{2 x ^{3}}{6}

Cancel

\frac{3 x ^{2} y}{6} : \frac{x ^{2} y}{2}

= \frac{x ^{2} y}{2} - \frac{2 x ^{3}}{6}

Cancel

\frac{2 x ^{3}}{6} : \frac{x ^{3}}{3}

= \frac{x ^{2} y}{2} - \frac{x ^{3}}{3}

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

\frac{( - 3 x + 12 )}{x ( x - 3 )}

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

\frac{( b s + a ) ^{2}}{s ^{3}}

e^{x^{2}} (\frac{d y}{d x} + 2 x y)

What is expand (x^2(3y-2x))/6 ?
The solution to expand (x^2(3y-2x))/6 is (x^2y)/2-(x^3)/3