# (4x+1)(3x-2)?

May 23, 2018

$12 {x}^{2} - 5 x - 2$

#### Explanation:

Use F.O.I.L. (First, Outside, Inside, Last). Multiply the first terms, $4 x$ and $3 x$, to get $12 {x}^{2}$. Then the outside term, $4 x$ and $- 2$, to get $- 8 x$.

Then the inside, $1$ and $3 x$, to get $3 x$. Finally, the last terms, $1$ and $- 2$, to get $- 2$. You now have

$12 {x}^{2} - 8 x + 3 x - 2$

This can be simplified to

$12 {x}^{2} - 5 x - 2$

May 23, 2018

$12 {x}^{2} - 5 x - 2$

#### Explanation:

$\text{each term in the second bracket is multiplied by}$
$\text{each term in the first bracket}$

$= \left(\textcolor{red}{4 x + 1}\right) \left(3 x - 2\right)$

$= \textcolor{red}{4 x} \left(3 x - 2\right) \textcolor{red}{+ 1} \left(3 x - 2\right) \leftarrow \textcolor{b l u e}{\text{distribute}}$

$= \left(\textcolor{red}{4 x} \times 3 x\right) + \left(\textcolor{red}{4 x} \times - 2\right) + \left(\textcolor{red}{1} \times 3 x\right) + \left(\textcolor{red}{1} \times - 2\right)$

$= 12 {x}^{2} \textcolor{b l u e}{- 8 x} \textcolor{b l u e}{+ 3 x} - 2 \leftarrow \textcolor{m a \ge n t a}{\text{collect like terms}}$

$= 12 {x}^{2} - 5 x - 2$