Final answer:
To expand the polynomial (a² - 4)(2a² - a - 1), we multiply each term in the first binomial by each term in the second binomial, sum the products, and combine like terms. The result is the polynomial 2a⁴ - 9a² + 4.
Step-by-step explanation:
To expand the polynomial (a² - 4)(2a² - a - 1), we use the distributive property, also known as the FOIL (First, Outside, Inside, Last) method. Each term in the first binomial is multiplied by each term in the second binomial, and the products are then summed.
Step-by-step expansion:
- (a²) * (2a²) = 2a⁴
- (a²) * (-a) = -a³
- (a²) * (-1) = -a²
- (-4) * (2a²) = -8a²
- (-4) * (-a) = 4a
- (-4) * (-1) = 4
Combine like terms:
- There's only one a⁴ term: 2a⁴.
- There are two a² terms: -a² - 8a² = -9a².
- The a terms (if any) do not have like terms, so -a³ and 4a remain unchanged, but they will cancel each other out since they are not present in the original polynomial.
- The constant term 4 remains unchanged.
Therefore, the expanded polynomial is 2a⁴ - 9a² + 4, which corresponds to option (a).