Answer :
Answer:
The third option
Step-by-step explanation:
Given
(a + 3)(- 2a² + 15a + 6b²)
Each term in the second factor is multiplied by each term in the first factor, that is
a(- 2a² + 15a + 6b²) + 3(- 2a² + 15a + 6b²) ← distribute both parenthesis
= - 2a³ + 15a² + 6ab² - 6a² + 45a + 18b² ← collect like terms
= - 2a³ + 9a² + 45a + 6ab² + 18b² → C
The product between the factors: (a+3) and (-2a²+15a+6b²) is equal to -2a³+9a²+45a+6ab²+18b².
Factoring
In math, the factoring or factorization is used to write an algebraic expression in factors.
The question gives the factors and asks your respective polynomial. For solving this exercise, you should calculate the multiplication between the factors: (a+3) and (-2a²+15a+6b²) and after that you should match the result with the options.
[tex](a+3) * (-2a^2+15a+6b^2)\\ \\ -2a^3+15a^2+6ab^2-6a^2+45a+18b^2\\ \\ -2a^3+9a^2+45a+6ab^2+18b^2\\[/tex]
Therefore, the found result matches with the equation 3.
Learn more about the factoring here:
brainly.com/question/11579257