Question

what is the product of $(3a + 2)(4a^2 - 2a + 9)?$
$12a^3 - 6a^2 + 23a + 18$
$12a^3 + 2a^2 + 23a + 18$
$12a^3 + 6a + 9$
$12a^3 - 2a + 18$

Explanation:

Step1: Distribute $3a$ to each term

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

Step2: Distribute $2$ to each term

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

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:

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