What is the product of a+3 and - 2a2+15a+6b2?

O-2a3+9a2+45a+2462

O-2a3+21a2+45a+2462

O - 2a3+9a2+45a+baba+1862

O-2a3+21a2+45a+6ab2+1862

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

Step-by-step explanation:

(a + 3) * (-2a^2 + 15a + 6b^2)

We open the brackets with (a + 3)

a (-2a^2 + 15a + 6b^2) + 3 (-2a^2 + 15a + 6b^2)

Opening the brackets

= a * - 2a^2 = - 2a^3

a * 15a = 15a^2

a * 6b^2 = 6ab^2

3 * - 2a^2 = - 6a^2

3 * 15a = 45a

3 * 6b^2 = 18b^2

Let's arrange those values weve gotten together, don't forget the signs each carry

= - 2a^3 + 15a^2 + 6ab^2 - 6a^2 + 45a + 18b^2

Collect the like terms

= - 2a^3 + 15a^2 - 6a^2 + 6ab^2 + 45a + 18b^2

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