Question

Multiply (x - 1)(x + 4x2 + 4x - 1) and combine like terms.

A. x³ + 4x² + 3x − 2
B. x³ + 4x² + 3x − 1
C. 4x³ + 4x² + 4x − 2
D. 4x³ + 4x² + 4x − 1

Answer 1

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.