# How do you multiply (7w - 3u - 6) ( 7w + 2)?

Jul 21, 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.

$\left(\textcolor{red}{7 w} - \textcolor{red}{3 u} - \textcolor{red}{6}\right) \left(\textcolor{b l u e}{7 w} + \textcolor{b l u e}{2}\right)$ becomes:

$\left(\textcolor{red}{7 w} \times \textcolor{b l u e}{7 w}\right) + \left(\textcolor{red}{7 w} \times \textcolor{b l u e}{2}\right) - \left(\textcolor{red}{3 u} \times \textcolor{b l u e}{7 w}\right) - \left(\textcolor{red}{3 u} \times \textcolor{b l u e}{2}\right) - \left(\textcolor{red}{6} \times \textcolor{b l u e}{7 w}\right) - \left(\textcolor{red}{6} \times \textcolor{b l u e}{2}\right)$

$49 {w}^{2} + 14 w - 21 u w - 6 u - 42 w - 12$

We can now group and combine like terms:

$49 {w}^{2} + 14 w - 42 w - 21 u w - 6 u - 12$

$49 {w}^{2} + \left(14 - 42\right) w - 21 u w - 6 u - 12$

$49 {w}^{2} + \left(- 28\right) w - 21 u w - 6 u - 12$

$49 {w}^{2} - 28 w - 21 u w - 6 u - 12$

Jul 21, 2017

Basically, use the distributive property of multiplication and after the multiplication is done, combine the same variables and simplify them.

#### Explanation:

It is the use of the distributive properties of multiplication (since the concepts are almost the same in Algebra) and simplifying them altogether.

(7w - 3u - 6)(7w+2) = 49w^2 -21uw -42w +14w - 6u -12 = 49w^2 - 21uw -28w - 6u -12