Final answer:
To simplify the given expression, expand the cubes and squares and then combine the like terms.
Step-by-step explanation:
To simplify the expression 2x²y(x - 3)³ + 4xy³(x - 3)², we can apply the distributive property and simplify each term separately.
For the first term, 2x²y(x - 3)³, we can expand the cube to get 2x²y(x³ - 3x² + 9x - 27).
For the second term, 4xy³(x - 3)², we can expand the square to get 4xy³(x² - 6x + 9).
Now, we can combine like terms by adding the coefficients of the similar terms. The simplified expression is 2x⁴y - 6x³y + 18x²y - 54xy + 4x²y³ - 24xy⁴ + 36xy³.