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

Apr 27, 2017

$6 {a}^{4} + 18 {a}^{3} + 12 {a}^{2}$

#### Explanation:

First, apply the distributive property to get:
$\left(2 {a}^{2} + 2 a\right) \left(3 {a}^{2} + 6 a\right)$

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

You then have $6 {a}^{4} + 12 {a}^{3} + 6 {a}^{3} + 12 {a}^{2} = 6 {a}^{4} + 18 {a}^{3} + 12 {a}^{2}$

You can also apply FOIL first and then multiply everything by 2.
$2 \left(3 {a}^{4} + 6 {a}^{3} + 3 {a}^{3} + 6 {a}^{2}\right)$
$= 2 \left(3 {a}^{4} + 9 {a}^{3} + 6 {a}^{2}\right)$
$= 6 {a}^{4} + 18 {a}^{3} + 12 {a}^{2}$