Which expression us equivalent to this polynomial expression? (2a - 3b) (2a^2 + 6b^2) + ( 6a^2b + 12ab^2 - 7b^3)

D. 4a³ + 24ab² - 25b³

Step-by-step explanation:

Simplify the given polynomial expression to find its equivalent as follows:

(2a - 3b)(2a² + 6b²) + (6a²b + 12ab² - 7b³)

2a(2a² + 6b²) -3b(2a² + 6b²) + (6a²b + 12ab² - 7b³)

4a³ + 12ab² - 6a²b - 18b³ + 6a²b + 12ab² - 7b³

Collect like terms

4a³ - 6a²b + 6a²b + 12ab² + 12ab² - 18b³ - 7b³

4a³ + 24ab² - 25b³

Therefore, 4a³ + 24ab² - 25b³ is equivalent to the polynomial expression, (2a - 3b)(2a² + 6b²) + (6a²b + 12ab² - 7b³).