Final answer:
To simplify the expression (4(x² - 3x - 1) - 4(-x² - 2x - 5)), distribute and combine like terms to get the simplified form 8x² - 4x + 4.
Step-by-step explanation:
To simplify the expression (4(x² - 3x - 1) - 4(-x² - 2x - 5)), we need to apply the distributive property and simplify each term within the parentheses.
First, distribute 4 to each term inside the first set of parentheses:
4x² - 12x - 4 - 4(-x² - 2x - 5)
Simplify further by distributing -4 to each term inside the second set of parentheses:
4x² - 12x - 4 + 4x² + 8x + 20
Combine like terms:
8x² - 4x - 16 + 20
The simplified form is 8x² - 4x + 4.