27x³ - 27x² y + 9xy²-y³ + 20x³ - 15x² y + 4xy² - 3y³ - 10x³ - 12x² y +5xy² - y³

To simplify the given expression, we can combine like terms.

Starting with the x^3 terms: 27x³ + 20x³ - 10x³ = 37x³

Next, let's combine the x^2 y terms:

• 27x² y - 15x² y - 12x² y = -54x² y

Then, let's combine the xy² terms: 9xy² + 4xy² + 5xy² = 18xy²

Finally, let's combine the y^3 terms:

• y³ - 3y³ - y³ = -5y³

Putting it all together, the simplified expression is: 37x³ - 54x² y + 18xy² - 5y³.