# How do you find the product of (3q+2)(9q^2-12q+4)?

Sep 7, 2016

$27 {q}^{3} - 18 {q}^{2} - 12 q + 8$

#### Explanation:

We must ensure that each term in the 2nd bracket is multiplied by each term in the 1st bracket.
This can be done as follows.

$\left(\textcolor{red}{3 q + 2}\right) \left(9 {q}^{2} - 12 q + 4\right)$

$= \textcolor{red}{3 q} \left(9 {q}^{2} - 12 q + 4\right) \textcolor{red}{+ 2} \left(9 {q}^{2} - 12 q + 4\right)$

now distribute each bracket.

$= 27 {q}^{3} - 36 {q}^{2} + 12 q + 18 {q}^{2} - 24 q + 8$

and collecting like terms gives.

$27 {q}^{3} + \left(- 36 {q}^{2} + 18 {q}^{2}\right) + \left(12 q - 24 q\right) + 8$

$= 27 {q}^{3} - 18 {q}^{2} - 12 q + 8 \leftarrow \text{ is the result of the product}$