Question

answer as soon as possible
What is the product of a+3 and −2a^2+15a+6b^2?
A −2a^3+9a^2+45a+24b^2
B −2a^3+21a^2+45a+24b^2
C −2a^3+9a^2+45a+6ab^2+18b^2
D −2a^3+21a^2+45a+6ab^2+18b^2

Answer 1

Answer:

C −2a^3+9a^2+45a+6ab^2+18b^2

Step-by-step explanation:

(a+3) ( −2a^2+15a+6b^2)

Distribute the a to the large term in parentheses and the 3 to the large term in parentheses

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

−2a^3+15a^2+6ab^2 −6a^2+45a+18b^2

Combine like terms

−2a^3+15a^2−6a^2+6ab^2 +45a+18b^2

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

Answer 2

Answer:

C. $-2a^3+9a^2+45a+6ab^2+18b^2$

Step-by-step explanation:

Product of $(a+3)$ and $(-2a^2+15a+6b^2)$

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

By distributive property,

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

Again by distributive property,

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

Combine like terms,

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

Hence, Option 'C' is correct.