What is expand ((-3x^2y+1)^3)/(27x^8) ?

The solution to expand ((-3x^2y+1)^3)/(27x^8) is -(y^3)/(x^2)+(y^2)/(x^4)-y/(3x^6)+1/(27x^8)

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expand ((-3x^2y+1)^3)/(27x^8)

expand

\frac{( - 3 x ^{2} y + 1 ) ^{3}}{27 x ^{8}}

- \frac{y ^{3}}{x ^{2}} + \frac{y ^{2}}{x ^{4}} - \frac{y}{3 x ^{6}} + \frac{1}{27 x ^{8}}

Solution steps

\frac{( - 3 x ^{2} y + 1 ) ^{3}}{27 x ^{8}}

(- 3 x^{2} y + 1)^{3} = - 27 x^{6} y^{3} + 27 x^{4} y^{2} - 9 x^{2} y + 1

= \frac{( - 27 x ^{6} y ^{3} + 27 x ^{4} y ^{2} - 9 x ^{2} y + 1 )}{27 x ^{8}}

Remove parentheses:

(- a) = - a

= \frac{- 27 x ^{6} y ^{3} + 27 x ^{4} y ^{2} - 9 x ^{2} y + 1}{27 x ^{8}}

Apply the fraction rule:

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

\frac{- 27 x ^{6} y ^{3} + 27 x ^{4} y ^{2} - 9 x ^{2} y + 1}{27 x ^{8}} = - \frac{27 x ^{6} y ^{3}}{27 x ^{8}} + \frac{27 x ^{4} y ^{2}}{27 x ^{8}} - \frac{9 x ^{2} y}{27 x ^{8}} + \frac{1}{27 x ^{8}}

= - \frac{27 x ^{6} y ^{3}}{27 x ^{8}} + \frac{27 x ^{4} y ^{2}}{27 x ^{8}} - \frac{9 x ^{2} y}{27 x ^{8}} + \frac{1}{27 x ^{8}}

Cancel

\frac{27 x ^{6} y ^{3}}{27 x ^{8}} : \frac{y ^{3}}{x ^{2}}

= - \frac{y ^{3}}{x ^{2}} + \frac{27 x ^{4} y ^{2}}{27 x ^{8}} - \frac{9 x ^{2} y}{27 x ^{8}} + \frac{1}{27 x ^{8}}

Cancel

\frac{27 x ^{4} y ^{2}}{27 x ^{8}} : \frac{y ^{2}}{x ^{4}}

= - \frac{y ^{3}}{x ^{2}} + \frac{y ^{2}}{x ^{4}} - \frac{9 x ^{2} y}{27 x ^{8}} + \frac{1}{27 x ^{8}}

Cancel

\frac{9 x ^{2} y}{27 x ^{8}} : \frac{y}{3 x ^{6}}

= - \frac{y ^{3}}{x ^{2}} + \frac{y ^{2}}{x ^{4}} - \frac{y}{3 x ^{6}} + \frac{1}{27 x ^{8}}

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

(2 + - 9)^{3}

- \frac{ln ( x - 3 )}{ln ( e )} + e^{l n (- 2)}

\frac{5 x ^{2} - 2}{x ^{3} ( x + 1 ) ^{2}}

8 \cdot 1 \frac{4}{5} + 2.4 \cdot \frac{1}{4} - \frac{1}{5} (0.02 + \frac{3}{100})

What is expand ((-3x^2y+1)^3)/(27x^8) ?
The solution to expand ((-3x^2y+1)^3)/(27x^8) is -(y^3)/(x^2)+(y^2)/(x^4)-y/(3x^6)+1/(27x^8)