What is expand-(2(3x^2y^2dx+4x^3y-12dy))/y ?

The solution to expand-(2(3x^2y^2dx+4x^3y-12dy))/y is -6x^2ydx-8x^3+(24dy)/y

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expand-(2(3x^2y^2dx+4x^3y-12dy))/y

expand

- \frac{2 ( 3 x ^{2} y ^{2} d x + 4 x ^{3} y - 12 d y )}{y}

- 6 x^{2} y d x - 8 x^{3} + \frac{24 d y}{y}

Solution steps

- \frac{2 ( 3 x ^{2} y ^{2} d x + 4 x ^{3} y - 12 d y )}{y}

Expand

2 (3 x^{2} y^{2} d x + 4 x^{3} y - 12 d y) : 6 x^{2} y^{2} d x + 8 x^{3} y - 24 d y

= - \frac{8 x ^{3} y + 6 x ^{2} y ^{2} d x - 24 d y}{y}

Apply the fraction rule:

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

\frac{6 x ^{2} y ^{2} d x + 8 x ^{3} y - 24 d y}{y} = - (\frac{6 x ^{2} y ^{2} d x}{y}) - (\frac{8 x ^{3} y}{y}) - (- \frac{24 d y}{y})

= - (\frac{6 x ^{2} y ^{2} d x}{y}) - (\frac{8 x ^{3} y}{y}) - (- \frac{24 d y}{y})

Remove parentheses:

(a) = a, - (- a) = a

= - \frac{6 x ^{2} y ^{2} d x}{y} - \frac{8 x ^{3} y}{y} + \frac{24 d y}{y}

Cancel

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

= - 6 x^{2} y d x - \frac{8 x ^{3} y}{y} + \frac{24 d y}{y}

Cancel

\frac{8 x ^{3} y}{y} : 8 x^{3}

= - 6 x^{2} y d x - 8 x^{3} + \frac{24 d y}{y}

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What is expand-(2(3x^2y^2dx+4x^3y-12dy))/y ?
The solution to expand-(2(3x^2y^2dx+4x^3y-12dy))/y is -6x^2ydx-8x^3+(24dy)/y