Simplify:

To simplify, we will proceed as follows:

a2b2(a + 2b)(3a + b)

$=\left[a^{2} b^{2}(a+2 b)\right](3 a+b)$

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

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

$=3 a^{4} b^{2}+6 a^{3} b^{3}+a^{3} b^{3}+2 a^{2} b^{4}$

$=3 a^{4} b^{2}+7 a^{3} b^{3}+2 a^{2} b^{4}$

Thus, the answer is $3 a^{4} b^{2}+7 a^{3} b^{3}+2 a^{2} b^{4}$.