Simplify 2a^2b^3 (4a^2 + 3ab^2 - ab) = ?

A. 8a^4b^5 + 3a^3b^5 + 2a^3b^4 B. 8a^4b^5 + 3a^3b^5 - 2a^3b^4

C. 8a^4b^3 + 6a^3b^5 + 2a^3b^4 D. 8a^4b^3 + 6a^3b^5 - 2a^3b^4

D. 8a^4b^3 + 6a^3b^5 - 2a^3b^4

Step-by-step explanation:

To simplify the given expression, we must open up the parenthesis by multiplying the variable outside of it with all the individual elements in the parenthesis.

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

2a^2b^3 * 3ab^2 = 6a^3b^5

2a^2b^3 * - ab = - 2a^3b^4

Adding up the products

2a^2b^3 (4a^2 + 3ab^2 - ab) = 8a^4b^3 + 6a^3b^5 - 2a^3b^4

The answer is D

When multiplying like terms, we add the power

When dividing like terms, we subtract the powers