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

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When multiplying two algebraic expressions, we can apply the distributive property.

So, we multiply each term from the first expression (2a^2b) by each term from the second expression (3b^3 + 4b^5) as follows:

2a^2b * 3b^3 = 6a^2b^4
2a^2b * 4b^5 = 8a^2b^6

Combining these two terms, we have:

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

Thus, the multiplication of 2a^2b and (3b^3 + 4b^5) is 6a^2b^4 + 8a^2b^6.