What is expand ((-6+y^2)^2y)/8 ?

The solution to expand ((-6+y^2)^2y)/8 is (y^5)/8-(3y^3)/2+(9y)/2

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expand ((-6+y^2)^2y)/8

expand

\frac{( - 6 + y ^{2} ) ^{2} y}{8}

\frac{y ^{5}}{8} - \frac{3 y ^{3}}{2} + \frac{9 y}{2}

Solution steps

\frac{( - 6 + y ^{2} ) ^{2} y}{8}

(- 6 + y^{2})^{2} = 36 - 12 y^{2} + y^{4}

= \frac{y ( y ^{4} - 12 y ^{2} + 36 )}{8}

Expand

(36 - 12 y^{2} + y^{4}) y : 36 y - 12 y^{3} + y^{5}

= \frac{36 y - 12 y ^{3} + y ^{5}}{8}

Apply the fraction rule:

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

\frac{36 y - 12 y ^{3} + y ^{5}}{8} = \frac{36 y}{8} - \frac{12 y ^{3}}{8} + \frac{y ^{5}}{8}

= \frac{36 y}{8} - \frac{12 y ^{3}}{8} + \frac{y ^{5}}{8}

Cancel

\frac{36 y}{8} : \frac{9 y}{2}

= \frac{9 y}{2} - \frac{12 y ^{3}}{8} + \frac{y ^{5}}{8}

Cancel

\frac{12 y ^{3}}{8} : \frac{3 y ^{3}}{2}

= \frac{9 y}{2} - \frac{3 y ^{3}}{2} + \frac{y ^{5}}{8}

Rewrite in standard form

= \frac{y ^{5}}{8} - \frac{3 y ^{3}}{2} + \frac{9 y}{2}

\frac{x ( x + 1 ) d y}{d x}

\frac{( - \frac{10}{5} x ^{4} y ^{3} z ^{2} )}{( \frac{1}{2} y ^{3} )}

(\frac{- 21}{34} - \frac{16 x}{- 17})^{2}

(x^{2} + x + 1) (- 15 x^{2} + 15 x - \frac{3}{2})

11 z (- z + 11)

What is expand ((-6+y^2)^2y)/8 ?
The solution to expand ((-6+y^2)^2y)/8 is (y^5)/8-(3y^3)/2+(9y)/2