# How do you simplify the product (3x + 1)(4x^2 - 2x + 1) and write it in standard form?

Jun 4, 2017

See a solution 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.

$\left(\textcolor{red}{3 x} + \textcolor{red}{1}\right) \left(\textcolor{b l u e}{4 {x}^{2}} - \textcolor{b l u e}{2 x} + \textcolor{b l u e}{1}\right)$ becomes:

$\left(\textcolor{red}{3 x} \times \textcolor{b l u e}{4 {x}^{2}}\right) - \left(\textcolor{red}{3 x} \times \textcolor{b l u e}{2 x}\right) + \left(\textcolor{red}{3 x} \times \textcolor{b l u e}{1}\right) + \left(\textcolor{red}{1} \times \textcolor{b l u e}{4 {x}^{2}}\right) - \left(\textcolor{red}{1} \times \textcolor{b l u e}{2 x}\right) + \left(\textcolor{red}{1} \times \textcolor{b l u e}{1}\right)$

$12 {x}^{3} - 6 {x}^{2} + 3 x + 4 {x}^{2} - 2 x + 1$

We can now group and combine like terms:

$12 {x}^{3} - 6 {x}^{2} + 4 {x}^{2} + 3 x - 2 x + 1$

$12 {x}^{3} + \left(- 6 + 4\right) {x}^{2} + \left(3 - 2\right) x + 1$

$12 {x}^{3} + \left(- 2\right) {x}^{2} + 1 x + 1$

$12 {x}^{3} - 2 {x}^{2} + x + 1$