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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

(- y, z - 1, - 1) \cdot (1, 1, 1)

\frac{1}{3 - 1} - sin (3 - 1)

\frac{2 ( cos ( \frac{πn}{2} ) - 1 )}{π ^{2} n ^{2}}

\frac{17 ( P + Ds )}{34 s ^{2} + 17 s + 0.6}

\frac{x + 2 ( 2 x ^{2} + 1 ) + 1}{2 x ^{2} + 1}

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