Question

Which expression is equivalent to the polynomial expression (2a-3b)(2a²-6b²)?

1) (4a³-12ab²-6ab+18b³)
2) (4a³-12ab²+6ab-18b³)
3) (4a³+12ab²-6ab-18b³)
4) (4a³+12ab²+6ab+18b³)

Answer 1

The expression equivalent to (2a-3b)(2a²-6b²) is (4a³-12a²b-6ab+18b³).

Step-by-step explanation:

To find the expression that is equivalent to the polynomial expression (2a-3b)(2a²-6b²), we need to multiply each term from the first expression by each term from the second expression and combine like terms.

The first expression (2a-3b) has two terms, and the second expression (2a²-6b²) has two terms as well. So, when we multiply each term, we will have a total of four terms.

Multiplying the terms, we get: 4a³-12a²b-6ab+18b³.

Therefore, the equivalent expression is (4a³-12a²b-6ab+18b³).