1. Replace the asterisk $(*)$ in the expression $\left(x^{3}-2\right)^{2}+\left(x^{2}+*\right)^{2}$ with a monomial so that after squaring and combining like terms, there are four terms.
Solution. Replace the asterisk (*) with $2 x: \quad\left(x^{3}-2\right)^{2}+\left(x^{2}+2 x\right)^{2}=$ $x^{6}-4 x^{3}+4+x^{4}+4 x^{3}+4 x^{2}=x^{6}+x^{4}+4 x^{2}+4$