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.
