Question

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

Answer 1

For this case we must find the product of the following expression:

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

We apply distributive property term to term:

`(a + 3) (- 2a ^ 2 + 15a + 6b ^ 2) =\\-2a ^ 2 * a + 15a * a + 6b ^ 2 * a-6a ^ 2 + 45a + 18b ^ 2 =\\-2a ^ 3 + 15a ^ 2 + 6ab ^ 2-6a ^ 2 + 45a + 18b ^ 2=`

We add similar terms:

`-2a ^ 3 + (15-6) a ^ 2 + 6ab ^ 2 + 45a + 18b ^ 2 =\\-2a ^ 3 + 9a ^ 2 + 6ab ^ 2 + 45a + 18b ^ 2 =`

Finally, the expression is as:

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

Answeer:

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