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

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

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.

Answer 2

C −2a^3+9a^2+45a+6ab^2+18b^2

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