What is expand ((y^3)/2-1/(2y^3))^2 ?

The solution to expand ((y^3)/2-1/(2y^3))^2 is (y^{12}-2y^6+1)/(4y^6)

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expand ((y^3)/2-1/(2y^3))^2

expand

(\frac{y ^{3}}{2} - \frac{1}{2 y ^{3}})^{2}

\frac{y ^{12} - 2 y ^{6} + 1}{4 y ^{6}}

Solution steps

(\frac{y ^{3}}{2} - \frac{1}{2 y ^{3}})^{2}

Apply Perfect Square Formula:

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

(\frac{y ^{3}}{2} - \frac{1}{2 y ^{3}})^{2} = (\frac{y ^{3}}{2})^{2} - 2 \cdot \frac{y ^{3}}{2} \cdot \frac{1}{2 y ^{3}} + (\frac{1}{2 y ^{3}})^{2}

= (\frac{y ^{3}}{2})^{2} - 2 \cdot \frac{y ^{3}}{2} \cdot \frac{1}{2 y ^{3}} + (\frac{1}{2 y ^{3}})^{2}

Simplify

(\frac{y ^{3}}{2})^{2} - 2 \cdot \frac{y ^{3}}{2} \cdot \frac{1}{2 y ^{3}} + (\frac{1}{2 y ^{3}})^{2} : \frac{y ^{12} - 2 y ^{6} + 1}{4 y ^{6}}

= \frac{y ^{12} - 2 y ^{6} + 1}{4 y ^{6}}

\frac{d ^{2}}{d y d x} ((f (y, x)) (x^{2} + 5 x y + sin (x) + 7 e^{x}))

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

(3 x + 9 y = 4,) (2 x - y = 2)

(x y - 2 x + 4 y - 8) d y - (x y + 3 x - y - 3) d x

- \frac{1}{8} (10 - x) + \frac{x}{2 π}

What is expand ((y^3)/2-1/(2y^3))^2 ?
The solution to expand ((y^3)/2-1/(2y^3))^2 is (y^{12}-2y^6+1)/(4y^6)