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

Explanation:

Step1: Use distributive property

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

Step2: Multiply each term

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

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:

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