\[(a + 2b)(2b - a) + (a + 3b)^{2} =\]
\[= (2b + a)(2b - a) + a^{2} + 2 \cdot 3ab + (3b)^{2} =\]
\[= (2b)^{2} - a^{2} + a^{2} + 6ab + 9b^{2} =\]
\[= 4b^{2} + 6ab + 9b^{2} =\]
\[= 13b^{2} + 6ab = b(6a + 13b)\text{.\ }\]