What is expand ((16x^2-1)(16x^2-1))/(64x^2) ?

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

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expand ((16x^2-1)(16x^2-1))/(64x^2)

expand

\frac{( 16 x ^{2} - 1 ) ( 16 x ^{2} - 1 )}{64 x ^{2}}

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

Solution steps

\frac{( 16 x ^{2} - 1 ) ( 16 x ^{2} - 1 )}{64 x ^{2}}

(16 x^{2} - 1) (16 x^{2} - 1) = (16 x^{2} - 1)^{2}

= \frac{( 16 x ^{2} - 1 ) ^{2}}{64 x ^{2}}

(16 x^{2} - 1)^{2} = 256 x^{4} - 32 x^{2} + 1

= \frac{256 x ^{4} - 32 x ^{2} + 1}{64 x ^{2}}

Apply the fraction rule:

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

\frac{256 x ^{4} - 32 x ^{2} + 1}{64 x ^{2}} = \frac{256 x ^{4}}{64 x ^{2}} - \frac{32 x ^{2}}{64 x ^{2}} + \frac{1}{64 x ^{2}}

= \frac{256 x ^{4}}{64 x ^{2}} - \frac{32 x ^{2}}{64 x ^{2}} + \frac{1}{64 x ^{2}}

Cancel

\frac{256 x ^{4}}{64 x ^{2}} : 4 x^{2}

= 4 x^{2} - \frac{32 x ^{2}}{64 x ^{2}} + \frac{1}{64 x ^{2}}

Cancel

\frac{32 x ^{2}}{64 x ^{2}} : \frac{1}{2}

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

\frac{\partial}{\partial y} (4 e^{y}) + e^{y} (2 x + 4 y)

\frac{d}{d t} ((x) (2 sinh (t) + 3 t^{2}))

\frac{( x ^{n + 1} - ( n + 1 ) x + n )}{x - 1}

6 sin (30 (t + 2))

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

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