What is expand ((y^4-1)^2)/(4y^4) ?

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

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expand ((y^4-1)^2)/(4y^4)

expand

\frac{( y ^{4} - 1 ) ^{2}}{4 y ^{4}}

\frac{y ^{4}}{4} - \frac{1}{2} + \frac{1}{4 y ^{4}}

Solution steps

\frac{( y ^{4} - 1 ) ^{2}}{4 y ^{4}}

(y^{4} - 1)^{2} = y^{8} - 2 y^{4} + 1

= \frac{y ^{8} - 2 y ^{4} + 1}{4 y ^{4}}

Apply the fraction rule:

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

\frac{y ^{8} - 2 y ^{4} + 1}{4 y ^{4}} = \frac{y ^{8}}{4 y ^{4}} - \frac{2 y ^{4}}{4 y ^{4}} + \frac{1}{4 y ^{4}}

= \frac{y ^{8}}{4 y ^{4}} - \frac{2 y ^{4}}{4 y ^{4}} + \frac{1}{4 y ^{4}}

Cancel

\frac{y ^{8}}{4 y ^{4}} : \frac{y ^{4}}{4}

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

Cancel

\frac{2 y ^{4}}{4 y ^{4}} : \frac{1}{2}

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

\frac{( 3 n ) ( 3 n + 1 )}{( 3 n - 1 ) ( 3 n + 2 )}

(y + x (x^{2} + y^{2})^{2}) d x + (y (x^{2} + y^{2})^{2} - x)

\frac{s}{( s - 1 ) ( s + 2 )}

\frac{1}{( x - 3 ) ^{5}}

\frac{2 s ^{3} - 3 s ^{2} + 10 s - 12}{( s ^{2} + 1 ) ( s - 2 ) ^{2}}

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