multiply 2a^2b (3b^3 + 4b^5)

To multiply 2a^2b with (3b^3 + 4b^5), we distribute the 2a^2b to each term within the parentheses:

2a^2b * 3b^3 = 6a^2b * b^3 = 6a^2b^4

2a^2b * 4b^5 = 8a^2b * b^5 = 8a^2b^6

So the final result is:

6a^2b^4 + 8a^2b^6