# How do you simplify (6x + 2)(2x^2 - 6x + 1)?

Feb 20, 2017

See the entire simplification process below:

#### Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{6 x} + \textcolor{red}{2}\right) \left(\textcolor{b l u e}{2 {x}^{2}} - \textcolor{b l u e}{6 x} + \textcolor{b l u e}{3}\right)$ becomes:

$\left(\textcolor{red}{6 x} \times \textcolor{b l u e}{2 {x}^{2}}\right) - \left(\textcolor{red}{6 x} \times \textcolor{b l u e}{6 x}\right) + \left(\textcolor{red}{6 x} \times \textcolor{b l u e}{1}\right) + \left(\textcolor{red}{2} \times \textcolor{b l u e}{2 {x}^{2}}\right) - \left(\textcolor{red}{2} \times \textcolor{b l u e}{6 x}\right) + \left(\textcolor{red}{2} \times \textcolor{b l u e}{1}\right)$

$12 {x}^{3} - 36 {x}^{2} + 6 x + 4 {x}^{2} - 12 x + 2$

We can now group and combine like terms:

$12 {x}^{3} - 36 {x}^{2} + 4 {x}^{2} + 6 x - 12 x + 2$

$12 {x}^{3} + \left(- 36 + 4\right) {x}^{2} + \left(6 - 12\right) x + 2$

$12 {x}^{3} - 32 {x}^{2} - 6 x + 2$