Multiplying two bivariate polynomials using FFT Consider two bivariate polynomials of degree at most $n − 1$ in each variable:
$$
F(x,y) = \sum_{i,j=0}^{n-1} f_{i,j} x^iy^j \quad\text{and}\quad G(x,y) = \sum_{i,j=0}^{n-1} g_{i,j} x^iy^j
$$
Show how to compute the product polynomial in $O(n^3 \log n)$ time.

Can anybody briefly explain the solution please?
The product is
$$
F(x,y) G(x,y) = \sum_{i=0}^{2n-2} x^i \sum_{i'=0}^{n-1} \left(\sum_{j=0}^{n-1} f_{i',j} y^j \right) \left(\sum_{j=0}^{n-1} g_{i-i',j} y^j\right).
$$
You take it from here.