Question

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

Answer 1

Answer:

-2a³+9a²+45a+6ab²+18b²

Step-by-step explanation:

(a+3)(-2a²+15a+6b²)

Distribute the a:

-2a³+15a²+6ab²

Then distribute the 3:

-6a²+45a+18b²

Now add both of the results together:

-2a³+15a²+6ab²-6a²+45a+18b²

Combine like terms:

-2a³+9a²+45a+6ab²+18b²

Answer 2

Answer:

  (c)  −2a^3+9a^2+45a+6ab^2+18b^2

Step-by-step explanation:

Examination of the answer choices shows us we only need to be concerned with the a^2 term and the b^2 term.

The a^2 term will be the sum of products ...

  3(-2a^2) +a(15a) = (-6 +15)a^2 = +9a^2

The b^2 term will be the product ...

  3(6b^2) = 18b^2

These terms are sufficient to identify choice C as the correct answer choice.

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Additional comment

It can often work well to develop the product of polynomials by considering the terms that must contribute to a given product term. For a term containing a^2, the product of polynomial terms can have that degree if and only if it is the product of a constant and an a^2 term, or the product of two a^1 terms. The ways those products can be achieved are shown in the above working.