What is expand ((4x^6-1)^2)/(16x^6) ?

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

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expand ((4x^6-1)^2)/(16x^6)

expand

\frac{( 4 x ^{6} - 1 ) ^{2}}{16 x ^{6}}

x^{6} - \frac{1}{2} + \frac{1}{16 x ^{6}}

Solution steps

\frac{( 4 x ^{6} - 1 ) ^{2}}{16 x ^{6}}

(4 x^{6} - 1)^{2} = 16 x^{12} - 8 x^{6} + 1

= \frac{16 x ^{12} - 8 x ^{6} + 1}{16 x ^{6}}

Apply the fraction rule:

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

\frac{16 x ^{12} - 8 x ^{6} + 1}{16 x ^{6}} = \frac{16 x ^{12}}{16 x ^{6}} - \frac{8 x ^{6}}{16 x ^{6}} + \frac{1}{16 x ^{6}}

= \frac{16 x ^{12}}{16 x ^{6}} - \frac{8 x ^{6}}{16 x ^{6}} + \frac{1}{16 x ^{6}}

Cancel

\frac{16 x ^{12}}{16 x ^{6}} : x^{6}

= x^{6} - \frac{8 x ^{6}}{16 x ^{6}} + \frac{1}{16 x ^{6}}

Cancel

\frac{8 x ^{6}}{16 x ^{6}} : \frac{1}{2}

= x^{6} - \frac{1}{2} + \frac{1}{16 x ^{6}}

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