# How do you simplify 2 - 5(3t - 4)?

Nov 19, 2015

$22 - 15 t$

#### Explanation:

the 5 multiplies everything inside the brackets so you have:

$2 - \left(5 \times 3 t - 5 \times 4\right)$

$2 - \left(15 t - 20\right)$

But that is not the end of it! You have a minus in front of the bracket.
This is the same as multiplying everything inside the brackets by (-1).

By the way, another way of looking at ' plus ' is as 'put with'; and at subtract as 'remove from':

Now we have :

$2 - 1 \left(15 t - 20\right)$

Just think about the $- 1 \left(15 t - 20\right)$ on its own for now

We have:

$\left(- 1 \times 15 t\right) - \left(- 1 \times 20\right)$

$\left(- 15 t\right) - \left(- 20\right)$

Negative times negative give you a positive so we have
$- 15 t + 20$

so $2 - \left(15 t - 20\right)$ becomes $\textcolor{w h i t e}{\times} 2 - 15 t + 20$

regrouping gives

$- 15 t + 2 + 20$

$- 15 t + 22$ which is the same as $22 - 15 t$