Question

what is the product of (3a + 2)(4a² − 2a + 9)?
12a³ − 2a + 18
12a³ + 6a + 9
12a³ − 6a² + 23a + 18
12a³ + 2a² + 23a + 18

Explanation:

Step1: Distribute $3a$ to each term

$3a \times 4a^2 + 3a \times (-2a) + 3a \times 9 = 12a^3 - 6a^2 + 27a$

Step2: Distribute $2$ to each term

$2 \times 4a^2 + 2 \times (-2a) + 2 \times 9 = 8a^2 - 4a + 18$

Step3: Combine all resulting terms

$12a^3 - 6a^2 + 27a + 8a^2 - 4a + 18$

Step4: Combine like terms

$12a^3 + (-6a^2+8a^2) + (27a-4a) + 18 = 12a^3 + 2a^2 + 23a + 18$

Answer:

D. $12a^3 + 2a^2 + 23a + 18$