Question

what is the product of a+3 and -2a²+15a+6b²? -2a³+9a²+45a+24b² -2a³+21a²+45a+24b² -2a³+9a²+45a+6ab²+18b² -2a³+21a²+45a+6ab²+18b²

Explanation:

Step1: Distribute each term

Multiply $(a+3)$ by each term in $-2a^2+15a+6b^2$.
$$(a)(-2a^2) + (a)(15a) + (a)(6b^2) + 3(-2a^2) + 3(15a) + 3(6b^2)$$

Step2: Calculate individual products

Compute each multiplication.
$$-2a^3 + 15a^2 + 6ab^2 -6a^2 + 45a + 18b^2$$

Step3: Combine like terms

Add the $a^2$ terms together.
$$-2a^3 + (15a^2-6a^2) + 6ab^2 + 45a + 18b^2 = -2a^3+9a^2+6ab^2+45a+18b^2$$

Answer:

$\boldsymbol{-2a^3+9a^2+45a+6ab^2+18b^2}$ (matches the second option)