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

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

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

expand

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

\frac{x ^{4}}{16} - \frac{1}{2} + \frac{1}{x ^{4}}

Solution steps

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

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

= \frac{x ^{8} - 8 x ^{4} + 16}{16 x ^{4}}

Apply the fraction rule:

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

\frac{x ^{8} - 8 x ^{4} + 16}{16 x ^{4}} = \frac{x ^{8}}{16 x ^{4}} - \frac{8 x ^{4}}{16 x ^{4}} + \frac{16}{16 x ^{4}}

= \frac{x ^{8}}{16 x ^{4}} - \frac{8 x ^{4}}{16 x ^{4}} + \frac{16}{16 x ^{4}}

Cancel

\frac{x ^{8}}{16 x ^{4}} : \frac{x ^{4}}{16}

= \frac{x ^{4}}{16} - \frac{8 x ^{4}}{16 x ^{4}} + \frac{16}{16 x ^{4}}

Cancel

\frac{8 x ^{4}}{16 x ^{4}} : \frac{1}{2}

= \frac{x ^{4}}{16} - \frac{1}{2} + \frac{16}{16 x ^{4}}

Divide the numbers:

\frac{16}{16} = 1

= \frac{x ^{4}}{16} - \frac{1}{2} + \frac{1}{x ^{4}}

Dr (π r^{2} + a r)

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

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

\frac{x}{e ^{x^{2} - \frac{1}{2} x^{4} + \frac{1}{3} x^{6}}}

\frac{( k + 6 ) ( k + 4 )}{2}

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