Question

what is the product of $a + 3$ and $-2a^2 + 15a + 6b^2$?
$-2a^3 + 21a^2 + 45a + 6ab^2 + 18b^2$
$-2a^3 + 9a^2 + 45a + 6ab^2 + 18b^2$
$-2a^3 + 9a^2 + 45a + 24b^2$
$-2a^3 + 21a^2 + 45a + 24b^2$

Explanation:

Step1: Distribute $a$ to each term

$a(-2a^2 + 15a + 6b^2) = -2a^3 + 15a^2 + 6ab^2$

Step2: Distribute 3 to each term

$3(-2a^2 + 15a + 6b^2) = -6a^2 + 45a + 18b^2$

Step3: Combine like terms

$(-2a^3 + 15a^2 + 6ab^2) + (-6a^2 + 45a + 18b^2) = -2a^3 + (15a^2-6a^2) + 45a + 6ab^2 + 18b^2 = -2a^3 + 9a^2 + 45a + 6ab^2 + 18b^2$

Answer:

$-2a^3 + 9a^2 + 45a + 6ab^2 + 18b^2$