Multiplying two bivariate polynomials using FFT
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.