# How do you multiply (v - 3) ( 4v + 2)?

Feb 2, 2017

$4 {v}^{2} - 10 v - 6$

#### Explanation:

This is an extremely simple question that uses the algebraic property of distribution. You must 'distribute' separately each of the terms of the first factor with the second factor as shown below:

$\left(v - 3\right) \left(4 v + 2\right)$
$= \left(v \cdot \left(4 v + 2\right)\right) + \left(- 3 \cdot \left(4 v + 2\right)\right)$
$= \left(4 {v}^{2} + 2 v\right) + \left(- 12 v - 6\right)$
$= 4 {v}^{2} + 2 v - 12 v - 6$
$= 4 {v}^{2} - 10 v - 6$

Feb 2, 2017

$4 {v}^{2} - 10 v - 6$

#### Explanation:

Each term in the second bracket must be multiplied by each term in the first bracket, as shown below.

$\left(\textcolor{red}{v - 3}\right) \left(4 v + 2\right)$

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

distribute.

$= 4 {v}^{2} + 2 v - 12 v - 6$

collect like terms.

$= 4 {v}^{2} - 10 v - 6$

An alternative method is called FOIL. This is illustrated in the diagram.

$\text{Firsts } v \times 4 v = 4 {v}^{2}$

$\text{Outers } 2 \times v = 2 v$

$\text{ Inners } - 3 \times 4 v = - 12 v$

$\text{Lasts } - 3 \times 2 = - 6$

$4 {v}^{2} + 2 v - 12 v - 6 = 4 {v}^{2} - 10 v - 6$