Final Answer:
The simplified product of the expression (x - 1)(x + 4x² + 4x - 1) is x³ + 4x² + 3x − 2 (option A).
Step-by-step explanation:
Distribute the first term (x - 1) across each term in the second expression:
x * (x + 4x² + 4x - 1) = x² + 4x³ + 4x² - x
-1 * (x + 4x² + 4x - 1) = -x - 4x² - 4x + 1
Combine like terms:
(x² + 4x³ + 4x² - x) + (-x - 4x² - 4x + 1)
= 4x³ + (x² + 4x² - 4x²) + (-x - 4x) + 1
= x³ + 4x² - 5x + 1
Arrange the terms in descending order of exponents:
x³ + 4x² + 3x − 2
Therefore, the correct answer is option A.