To simplify the expression (8x + 2x³ - 4x²) - (4 + x³ + 6x), we can combine like terms:
First, distribute the negative sign to the terms within the parentheses:
(8x + 2x³ - 4x²) - (4 + x³ + 6x)
= 8x + 2x³ - 4x² - 4 - x³ - 6x
Next, group the like terms together:
(8x - 6x) + (2x³ - x³) + (-4x²) + (-4)
= 2x + x³ - 4x² - 4
So the simplified form of the expression is 2x + x³ - 4x² - 4.