What is expand (6x^4(-24x^6+25y^5))/(25y^9) ?

The solution to expand (6x^4(-24x^6+25y^5))/(25y^9) is -(144x^{10})/(25y^9)+(6x^4)/(y^4)

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expand (6x^4(-24x^6+25y^5))/(25y^9)

expand

\frac{6 x ^{4} ( - 24 x ^{6} + 25 y ^{5} )}{25 y ^{9}}

- \frac{144 x ^{10}}{25 y ^{9}} + \frac{6 x ^{4}}{y ^{4}}

Solution steps

\frac{6 x ^{4} ( - 24 x ^{6} + 25 y ^{5} )}{25 y ^{9}}

Expand

6 x^{4} (- 24 x^{6} + 25 y^{5}) : - 144 x^{10} + 150 x^{4} y^{5}

= \frac{- 144 x ^{10} + 150 x ^{4} y ^{5}}{25 y ^{9}}

Apply the fraction rule:

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

\frac{- 144 x ^{10} + 150 x ^{4} y ^{5}}{25 y ^{9}} = - \frac{144 x ^{10}}{25 y ^{9}} + \frac{150 x ^{4} y ^{5}}{25 y ^{9}}

= - \frac{144 x ^{10}}{25 y ^{9}} + \frac{150 x ^{4} y ^{5}}{25 y ^{9}}

Cancel

\frac{150 x ^{4} y ^{5}}{25 y ^{9}} : \frac{6 x ^{4}}{y ^{4}}

= - \frac{144 x ^{10}}{25 y ^{9}} + \frac{6 x ^{4}}{y ^{4}}

(x - 2) (x - 3) (x + 3)

\frac{2 x ^{3} - 6 x}{( x ^{2} + 1 ) ^{3}}

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

2 (- 4 - 3)

\frac{1}{2} H (t + \frac{π}{4}) sin (2 (t + \frac{π}{4})) + 2 sin (2 t)

What is expand (6x^4(-24x^6+25y^5))/(25y^9) ?
The solution to expand (6x^4(-24x^6+25y^5))/(25y^9) is -(144x^{10})/(25y^9)+(6x^4)/(y^4)