What is expand ((16x^6-9)^2)/(576x^6) ?

The solution to expand ((16x^6-9)^2)/(576x^6) is (4x^6)/9-1/2+9/(64x^6)

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expand ((16x^6-9)^2)/(576x^6)

expand

\frac{( 16 x ^{6} - 9 ) ^{2}}{576 x ^{6}}

\frac{4 x ^{6}}{9} - \frac{1}{2} + \frac{9}{64 x ^{6}}

Solution steps

\frac{( 16 x ^{6} - 9 ) ^{2}}{576 x ^{6}}

(16 x^{6} - 9)^{2} = 256 x^{12} - 288 x^{6} + 81

= \frac{256 x ^{12} - 288 x ^{6} + 81}{576 x ^{6}}

Apply the fraction rule:

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

\frac{256 x ^{12} - 288 x ^{6} + 81}{576 x ^{6}} = \frac{256 x ^{12}}{576 x ^{6}} - \frac{288 x ^{6}}{576 x ^{6}} + \frac{81}{576 x ^{6}}

= \frac{256 x ^{12}}{576 x ^{6}} - \frac{288 x ^{6}}{576 x ^{6}} + \frac{81}{576 x ^{6}}

Cancel

\frac{256 x ^{12}}{576 x ^{6}} : \frac{4 x ^{6}}{9}

= \frac{4 x ^{6}}{9} - \frac{288 x ^{6}}{576 x ^{6}} + \frac{81}{576 x ^{6}}

Cancel

\frac{288 x ^{6}}{576 x ^{6}} : \frac{1}{2}

= \frac{4 x ^{6}}{9} - \frac{1}{2} + \frac{81}{576 x ^{6}}

Cancel

\frac{81}{576 x ^{6}} : \frac{9}{64 x ^{6}}

= \frac{4 x ^{6}}{9} - \frac{1}{2} + \frac{9}{64 x ^{6}}

\frac{7 n ^{2} + n ^{4} - 4 x ^{3}}{( x ^{4} + n ^{4} ) ^{2}}

\frac{( x ^{4} - 4 ) ^{2}}{16 x ^{4}}

Dr (π r^{2} + a r)

\frac{1}{( 1 + 5 x ) ^{4}}

- 3 i x^{2} + (2 + 2 i) x + 2

What is expand ((16x^6-9)^2)/(576x^6) ?
The solution to expand ((16x^6-9)^2)/(576x^6) is (4x^6)/9-1/2+9/(64x^6)