What is expand (5x^2y(xyz^6+3x^4y^4z^4-5))/(z^2) ?

The solution to expand (5x^2y(xyz^6+3x^4y^4z^4-5))/(z^2) is 5x^3y^2z^4+15x^6y^5z^2-(25x^2y)/(z^2)

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expand (5x^2y(xyz^6+3x^4y^4z^4-5))/(z^2)

expand

\frac{5 x ^{2} y ( x y z ^{6} + 3 x ^{4} y ^{4} z ^{4} - 5 )}{z ^{2}}

5 x^{3} y^{2} z^{4} + 15 x^{6} y^{5} z^{2} - \frac{25 x ^{2} y}{z ^{2}}

Solution steps

\frac{5 x ^{2} y ( x y z ^{6} + 3 x ^{4} y ^{4} z ^{4} - 5 )}{z ^{2}}

Expand

5 x^{2} y (x y z^{6} + 3 x^{4} y^{4} z^{4} - 5) : 5 x^{3} y^{2} z^{6} + 15 x^{6} y^{5} z^{4} - 25 x^{2} y

= \frac{5 x ^{3} y ^{2} z ^{6} + 15 x ^{6} y ^{5} z ^{4} - 25 x ^{2} y}{z ^{2}}

Apply the fraction rule:

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

\frac{5 x ^{3} y ^{2} z ^{6} + 15 x ^{6} y ^{5} z ^{4} - 25 x ^{2} y}{z ^{2}} = \frac{5 x ^{3} y ^{2} z ^{6}}{z ^{2}} + \frac{15 x ^{6} y ^{5} z ^{4}}{z ^{2}} - \frac{25 x ^{2} y}{z ^{2}}

= \frac{5 x ^{3} y ^{2} z ^{6}}{z ^{2}} + \frac{15 x ^{6} y ^{5} z ^{4}}{z ^{2}} - \frac{25 x ^{2} y}{z ^{2}}

Cancel

\frac{5 x ^{3} y ^{2} z ^{6}}{z ^{2}} : 5 x^{3} y^{2} z^{4}

= 5 x^{3} y^{2} z^{4} + \frac{15 x ^{6} y ^{5} z ^{4}}{z ^{2}} - \frac{25 x ^{2} y}{z ^{2}}

Cancel

\frac{15 x ^{6} y ^{5} z ^{4}}{z ^{2}} : 15 x^{6} y^{5} z^{2}

= 5 x^{3} y^{2} z^{4} + 15 x^{6} y^{5} z^{2} - \frac{25 x ^{2} y}{z ^{2}}

1 + \frac{1}{2} (e^{- \frac{x}{20}} - e^{\frac{x}{20}})

\frac{- u - 1}{2 ( u ^{2} - u )}

- 4 y (x + \frac{( y - z )}{2})

\frac{x ( x - 1 ) ( x - 12 ) ( x - 21 ) ( x - 23 ) ( x - 24 )}{40824}

y = 2 x + 5

What is expand (5x^2y(xyz^6+3x^4y^4z^4-5))/(z^2) ?
The solution to expand (5x^2y(xyz^6+3x^4y^4z^4-5))/(z^2) is 5x^3y^2z^4+15x^6y^5z^2-(25x^2y)/(z^2)