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

Explanation:

Step1: Apply Distributive Property

Multiply (a) and (3) with each term in (-2a^{2}+15a + 6b^{2}) separately. First, multiply (a) by (-2a^{2}+15a + 6b^{2}): (a\times(-2a^{2})=-2a^{3}), (a\times15a = 15a^{2}), (a\times6b^{2}=6ab^{2}) Then, multiply (3) by (-2a^{2}+15a + 6b^{2}): (3\times(-2a^{2})=-6a^{2}), (3\times15a = 45a), (3\times6b^{2}=18b^{2})

Step2: Combine Like Terms

Now, combine the results from Step1: For the (a^{3}) term: (-2a^{3}) (only one term) For the (a^{2}) terms: (15a^{2}-6a^{2}=9a^{2}) For the (a) terms: (45a) (only one term) For the (ab^{2}) term: (6ab^{2}) (only one term) For the (b^{2}) term: (18b^{2}) (only one term)

Putting it all together: (-2a^{3}+9a^{2}+45a + 6ab^{2}+18b^{2})

Answer:

-2a³+9a²+45a+6ab²+18b² (the third option)