Transform the following polynomial into a product:

$$
2 a^{3}-3 a^{2} b-3 a b^{2}+2 b^{3}
$$
When summarizing powers with equal exponents, we can also take advantage of the fact that the coefficients in such pairs of terms are equal:

$$
\begin{gathered}
2\left(a^{3}+b^{3}\right)-3\left(a^{2} b+a b^{2}\right)=2(a+b)\left(a^{2}-a b+b^{2}\right)-3 a b(a+b)= \\
=(a+b)\left(2 a^{2}-2 a b+2 b^{2}-3 a b\right)
\end{gathered}
$$

The second parenthesis can be transformed as follows:

$$
2 a^{2}-a b+2 b^{2}-4 a b=a(2 a-b)-2 b(2 a-b)=(a-2 b)(2 a-b)
$$

Therefore, our polynomial in product form is

$$
(a+b)(a-2 b)(2 a-b)
$$

József Pusztai (Kaposvár, M. Táncsics Gymnasium, 2nd grade)