展开-(2(3x^2y^2dx+4x^3y-12dy))/y

解答

展开

- \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}

求解步骤

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

乘开

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}

使用分式法则:

\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})

去除括号:

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

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

消掉

\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}

消掉

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

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

e x p an d - 23 (2 x - 8 y + 5 z = - 8)

e x p an d sinh ((x + y) (x - y))

e x p an d cos (2 x) - sin (2 x) (\frac{π}{4} + 3 π)

e x p an d \frac{( m + 3 ) ( m - 3 )}{m ^{2} - 16}

e x p an d \frac{( e ^{x} - 1 ) ( e ^{2 y} - 1 )}{x y}