Rút gọn biểu thức:

To simplify the expression 4a²-8ab/2(2b-a)³, we can start by simplifying the denominator.

The denominator is 2(2b-a)³. To simplify this, we can expand the cube of the binomial (2b-a)³.

(2b-a)³ = (2b-a)(2b-a)(2b-a)
= (4b² - 2ab - 2ab + a²)(2b-a)
= (4b² - 4ab + a²)(2b-a)
= 8b³ - 8ab² + 2ab² - 2a³ + 4ab - a³
= 8b³ - 6ab² - 3a³ + 4ab

Now, we can substitute this simplified denominator back into the expression:

4a² - 8ab / 2(2b-a)³
= 4a² - 8ab / (8b³ - 6ab² - 3a³ + 4ab)

So, the simplified expression is (4a² - 8ab) / (8b³ - 6ab² - 3a³ + 4ab).