What is expand (x(2x^3+y))/(6y^2) ?

The solution to expand (x(2x^3+y))/(6y^2) is (x^4)/(3y^2)+x/(6y)

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expand (x(2x^3+y))/(6y^2)

expand

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

\frac{x ^{4}}{3 y ^{2}} + \frac{x}{6 y}

Solution steps

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

Expand

x (2 x^{3} + y) : 2 x^{4} + x y

= \frac{2 x ^{4} + x y}{6 y ^{2}}

Apply the fraction rule:

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

\frac{2 x ^{4} + x y}{6 y ^{2}} = \frac{2 x ^{4}}{6 y ^{2}} + \frac{x y}{6 y ^{2}}

= \frac{2 x ^{4}}{6 y ^{2}} + \frac{x y}{6 y ^{2}}

Cancel

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

= \frac{x ^{4}}{3 y ^{2}} + \frac{x y}{6 y ^{2}}

Cancel

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

= \frac{x ^{4}}{3 y ^{2}} + \frac{x}{6 y}

\frac{\frac{d}{d x} ( x ^{3} - 2 )}{( 4 x + 3 ) ( 6 x - 2 )}

(a + b) a^{3} - a^{2} b + a b^{2}

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

\frac{- S ^{3} - S}{4 ( S ^{4} + S ^{2} + 4 )}

(x^{2} - x - e^{3 x})^{2}

What is expand (x(2x^3+y))/(6y^2) ?
The solution to expand (x(2x^3+y))/(6y^2) is (x^4)/(3y^2)+x/(6y)