Find the product:

By horizontal method:

$\left(2 x^{2}-5 y^{2}\right) \times\left(x^{2}+3 y^{2}\right)$

$=2 x^{2}\left(x^{2}+3 y^{2}\right)-5 y^{2}\left(x^{2}+3 y^{2}\right)$

$=2 x^{4}+6 x^{2} y^{2}-5 x^{2} y^{2}-15 y^{4}$

$=2 x^{4}+x^{2} y^{2}-15 y^{4}$