What is expand ((y^3)/2-2/(y^3))^2 ?

The solution to expand ((y^3)/2-2/(y^3))^2 is (-8y^6+y^{12}+16)/(4y^6)

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expand ((y^3)/2-2/(y^3))^2

expand

(\frac{y ^{3}}{2} - \frac{2}{y ^{3}})^{2}

\frac{- 8 y ^{6} + y ^{12} + 16}{4 y ^{6}}

Solution steps

(\frac{y ^{3}}{2} - \frac{2}{y ^{3}})^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(\frac{y ^{3}}{2} - \frac{2}{y ^{3}})^{2} = (\frac{y ^{3}}{2})^{2} - 2 \cdot \frac{y ^{3}}{2} \cdot \frac{2}{y ^{3}} + (\frac{2}{y ^{3}})^{2}

= (\frac{y ^{3}}{2})^{2} - 2 \cdot \frac{y ^{3}}{2} \cdot \frac{2}{y ^{3}} + (\frac{2}{y ^{3}})^{2}

Simplify

(\frac{y ^{3}}{2})^{2} - 2 \cdot \frac{y ^{3}}{2} \cdot \frac{2}{y ^{3}} + (\frac{2}{y ^{3}})^{2} : \frac{- 8 y ^{6} + y ^{12} + 16}{4 y ^{6}}

= \frac{- 8 y ^{6} + y ^{12} + 16}{4 y ^{6}}

x (2 ln (x) + 1)

\frac{( x - a ) ( x - b ) ( x - a - d )}{( x - c ) ( x - d ) ( x - a - b )}

(2 x) (2 x)

A (- 4, 7) B (6, - 2)

What is expand ((y^3)/2-2/(y^3))^2 ?
The solution to expand ((y^3)/2-2/(y^3))^2 is (-8y^6+y^{12}+16)/(4y^6)