What is expand ((9y^6-1)^2)/(36y^6) ?

The solution to expand ((9y^6-1)^2)/(36y^6) is (9y^6)/4-1/2+1/(36y^6)

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expand ((9y^6-1)^2)/(36y^6)

expand

\frac{( 9 y ^{6} - 1 ) ^{2}}{36 y ^{6}}

\frac{9 y ^{6}}{4} - \frac{1}{2} + \frac{1}{36 y ^{6}}

Solution steps

\frac{( 9 y ^{6} - 1 ) ^{2}}{36 y ^{6}}

(9 y^{6} - 1)^{2} = 81 y^{12} - 18 y^{6} + 1

= \frac{81 y ^{12} - 18 y ^{6} + 1}{36 y ^{6}}

Apply the fraction rule:

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

\frac{81 y ^{12} - 18 y ^{6} + 1}{36 y ^{6}} = \frac{81 y ^{12}}{36 y ^{6}} - \frac{18 y ^{6}}{36 y ^{6}} + \frac{1}{36 y ^{6}}

= \frac{81 y ^{12}}{36 y ^{6}} - \frac{18 y ^{6}}{36 y ^{6}} + \frac{1}{36 y ^{6}}

Cancel

\frac{81 y ^{12}}{36 y ^{6}} : \frac{9 y ^{6}}{4}

= \frac{9 y ^{6}}{4} - \frac{18 y ^{6}}{36 y ^{6}} + \frac{1}{36 y ^{6}}

Cancel

\frac{18 y ^{6}}{36 y ^{6}} : \frac{1}{2}

= \frac{9 y ^{6}}{4} - \frac{1}{2} + \frac{1}{36 y ^{6}}

\frac{10}{( x + 1 ) ( x + 2 ) ( x ^{2} + 1 )}

(- 6 = 2) (- 4 + 10)

\frac{1}{x ^{2} ( x ^{2} + 4 )}

(\frac{3}{5})^{2}

(\frac{d}{d x} (x e^{2 x}) - 2)^{2}

What is expand ((9y^6-1)^2)/(36y^6) ?
The solution to expand ((9y^6-1)^2)/(36y^6) is (9y^6)/4-1/2+1/(36y^6)