1. Can we use the signs «+», «-», «$\cdot$» and several expressions $a^{4}$ and $a^{6}-1$ to obtain $a^{6} ?$
Solution. Yes, $-\left(a^{6}-1\right) \cdot\left(a^{6}-1\right)-\left(a^{6}-1\right)+a^{4} \cdot a^{4} \cdot a^{4}=a^{6}$.