Multiply:

To multiply, we will use distributive law as follows:

$\left(x^{2}+y^{2}\right)(3 a+2 b)$

$=x^{2}(3 a+2 b)+y^{2}(3 a+2 b)$

$=3 a x^{2}+2 b x^{2}+3 a y^{2}+2 b y^{2}$

Thus, the answer is $3 a x^{2}+2 b x^{2}+3 a y^{2}+2 b y^{2}$.