3. \(\left(\frac{1}{2}x^3+6x\right)^2=\)

\[\left(\frac{1}{2}x^3+6x\right)^2=\left(\frac{1}{2}x^3\right)^2+2\cdot\frac{1}{2}x^3\cdot6x+(6x)^2\]

\[=\frac{1}{4}x^6+6x^4+36x^2\]

Ответ: \(\frac{1}{4}x^6+6x^4+36x^2\).