Question

How do you multiply `2(a^2 + a)(3a^2 + 6a)`?

Answer 1

`6a^4+18a^3+12a^2`

Explanation:

First, apply the distributive property to get:
`(2a^2+2a)(3a^2+6a)`

Here, you can use FOIL to get all the terms.
F irst --> `2a^2\cdot 3a^2=6a^4`
O uter --> `2a^2\cdot 6a=12a^3`
I nner --> `2a\cdot 3a^2=6a^3`
L ast --> `2a\cdot 6a=12a^2`

You then have `6a^4+12a^3+6a^3+12a^2=6a^4+18a^3+12a^2`

You can also apply FOIL first and then multiply everything by 2.
`2(3a^4+6a^3+3a^3+6a^2)`
`=2(3a^4+9a^3+6a^2)`
`=6a^4+18a^3+12a^2`